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calculus task for 11 January 2020.Edited at 7am 11 January 2020.s is your student number.For group task s = 19107089.k = s mod 10000. T = s mod 100. m35 = s mod 35. m25 = s mod 25. m20 = s mod 20. m17 = s mod 17.m10 = s mod 10. m9 = s mod 9. m8 = s mod 8. m7 = s mod 7. m6 = s mod 6. m5 = s mod 5. m4 = s mod 4. m3 = s mod 3. m2 = s mod 2.Midterm part: 1 section: 1. Why do you need calculus?2. Find average of m2, m3, m4, and m5.3. Which English letter is the thickest?4. Find maximum area rectangle for the same perimeter. 5. What plane shape has maximum area for same perimeter?6. What is function?7. Do your project. 8. What is calculus of social media? 9. Study calculus of songs. 10. Solve Zimmermann problem: for m20 + 6.Improve these solutions: you cannot register here then submit your solutions to me.11. What is fractal? . Explain least-squares fit.. Apply for American citizenship: . Apply for scholarships, grants, fellowships of USA, Europe, Canada, Australia, Japan, etc. 15. Study. What is infinitely small value?. Explain continuity. . Discuss calculus news.(2015%E2%80%93present). Study general concepts of limit, continuity, derivative, integral, differential equation, partial derivative, and optimization. (mathematics). How is calculus used in computer science?-2 section: 21. Calculate limits: m8 = 0: Limn→∞sinn =m8 = 1: Limx→0sin1x=m8 = 2: Limx→0x =m8 = 3: Limx→01x=m8 = 4: Limx→01x2=m8 = 5: Limx→0xx=m8 = 6: Limx→1x2-3x+2x-1=m8 = 7: Limx→2x2-3x+2x-2=Use = 0: 22. When does limit exist? = 1: 23. List indeterminate forms.. Explain drone calculus. = 1: 25. What are the properties of the limit? (times constant, sum, product, quotient)m2 = 0: 26. Give the main methods for calculating limits. 27. Prepare to Dota2 gaming competition:. What is chaos?. What are the great limits of calculus? 1. 2. 30. Investigate continuity of the function:m7 = 0: xm7 = 1: xm7 = 2: 1xm7 = 3: 1x2m7 = 4: xxm7 = 5: x2-3x+2x-1m7 = 6: x2-3x+2x-2m2 = 1: 31. Give the properties of derivative: times constant, sum, product, quotient. m2 = 0: 32. Prove expression for derivative of x2 using limit. 33. Find derivatives of these functions:m4 = 0: exm4 = 1: xpm4 = 2: cos(x)m4 = 3: xnn. Increasing or decreasing: m5 = 0: -6xm5 = 1: 9xm5 = 2: sin(x)m5 = 3: cos(x)m5 = 4: tan(x)m3 = 0: 35. What is Mean Value Theorem? = 1: 36. Explain Rolle theorem. = 2: 37. Give Fermat theorem. (stationary_points)38. Concave or convex:m4 = 0: x3m4 = 1: -x3m4 = 2: cos(x)m4 = 3: sin(x)39. Find inflection point:m4 = 0: x3m4 = 1: -x3m4 = 2: cos(x)m4 = 3: sin(x)40. Enjoy calculus.-3 section: 41. Find min and Max.Find the largest area rectangle with perimeter of T meters.Calculate the largest area right-angled triangle with perimeter of T meters.Find maximum volume cylinder for surface area of T meters square.Calculate maximum volume cone for surface area of T meters square.Calculate maximum area scalene triangle with perimeter of T meters. 42. How does guitar string move?43. Explain power pyramid: USA, UK, EU, Australia, New Zealand, Japan, Korea, Singapore, Malaysia, Indonesia, China, India, Russia, etc.44. Why are some civilizations more successful than the others?45. Why are some people very massive?46. What are Brownian motion, random walk and how are they linked to Zimmermann problem?47. Predict results of 2019 rugby world cup: . Explain good country index.. Calculate (1+1/T)T.. Solve number puzzle for 3 + m8 digits. . Hack password. . Why can crazy people be good for calculus?53. Who is internet troll?54. Analyze these topics: . Why is there less freedom in the world?56. Will Trump be impeached? Why?57. How do we help Indonesia?58. Limx→pfx = L. f(x) = Tx + k. For any ε find δ, using ε – δ definition of the limit.59. Find the discriminant of the elliptic curve y2 = x3 + Lx + T.Here L = m10.. Find linear least-square approximation for your dataset. (2, m2), (3, m3), (4, m4) section:61. Why is there terror? Why is monopoly bad?62. Explain physics Nobel Prize 2019.63. Do Bernoulli experiment.64. Find the hangover for the s blocks in the blocks stacking problem. . Use 3T mod n to pass secret.Calculate 3T mod 19 and exchange secret information with your friend.. Calculate the largest prime number. . Do prime factorization of s.. (xx)' = 69. Calculate derivative, using Chain Rule for sin(Tx)70. Find partial derivatives. m2 = 0: x + ym2 = 1: xy71. Calculate total derivative.m2 = 0: x + ym2 = 1: xy72. Find implicit function derivative. Lx2 + Ty2 – k = 073. Calculate inverse function derivative y = Tx + L.74. Analyze y = Tx + L. Find gradient, intercept, derivative, parallel line, perpendicular line. 75. Explainm8 = 0: composite functionm8 = 1: inverse functionm8 = 2: implicit functionm8 = 3: algebraic functionm8 = 4: transcendental functionm8 = 5: special functionm8 = 6: exponential functionm8 = 7: logarithmic function76. Explainm6 = 0: natural numberm6 = 1: integerm6 = 2: rational numberm6 = 3: irrational numberm6 = 4: real numberm6 = 5: complex number77. Give Fundamental Theorem of Calculus.. Integrate.xTdxsinTx dx01xTdx01sinTxdx. eTxdx80. 01eTxdx section: 81. Calculate Riemann sum for integral 01x2dxfor T intervals. integrals:82. Calculate 1∞x-Tdx83. Find 01x-1TdxApplication of integrals:84. Calculate area bellow the curve f(x)=1+cos(Tx)@[1/s,1/k].abf(x)dxf(x)=1+cos(Tx)a = 1/s b = 1/k. Calculate area between the curves f(x)=1+cos(Tx) and g(x)= 1+sin(Tx)@[1/s,1/k].ab(fx-g(x))dx. Calculate average value, center of mass and moment of inertia of f(x)=1+cos(Tx)@[1/s,1/k].abfxdxb-aabfxxdxabfxdxabfxx2dx. Find arc length of f(x) a. -0.006x2+0.3x@[1/s,11-1/k], b. 1+cos(Tx)@[1/s,1/k], c. x2@[0,T].ab1+f'(x)2dx. Calculate revolutionary volume and surface area of f(x) = 1 + cos(Tx) @ [1/s, 1/k].πab(f(x))2dx2πabf(x)1+f'(x)2dx. Give the integration formulas: m4 = 0: Left and right rectanglesm4 = 1: Mid-rectanglesm4 = 2: Trapezoidal rulem4 = 3: Simpson rule90. Explain the integration error bounds: m4 = 0: Left and right rectanglesm4 = 1: Mid-rectanglesm4 = 2: Trapezoidal rulem4 = 3: Simpson rule91. Find fxdx using Heaviside method.fx=L1x2+m1x+n1x-a1x-b1x-c1=A1x-a1+B1x-b1+C1x-c1L1 = L = m10m1 = m = m35n1 = sa1 = a = m25b1 = Tc1 = e = m8 equations:Solve these differential equations:Ordinary differential equations: 92. y' = y using Euler method for m2 + 2 unitary steps.y(0) = 1.. y' = Ty94. Ty'' + my' + Ly = 0m = m35L = m10 function, Logistic growth, Learning curve:95. Calculate logistic function P(t) for i = L+1 and R = t = M = L+2.P(t)=MieRtM+ieRt-1 differential equations: 96. Solve heat equation and wave propagation equation for v = T.Series:Number series: 97. Find T! and T-th Fibonacci number. . Calculate a.c=1T(-1)cc b.c=1T1c c.c=1Tc-4 d.c=1Tc-6 e.c=0Tbc f.c=1Tc-2 g.c=1Tc-3 h.c=0T(-1)c2c+1 i.c=1Tc-5. Find c=0∞T-cFunctional series: 100. Find the convergence radius and the sum.c=0∞Txc-Final part: 6 section: Same as in physics:Significant figures:101. How many significant figures are there in your student number?102. How many significant figures are there in your T number?103. Give the number of significant figures of the number for your T.1: 87780002: 0.0005673: 806004: 0.000679005: 3460006: 0.0006737: 953280008: 9432580009: 0.00077410: 990011: 98789012: 0.000056113: 9403460014: 90065354015: 0.00546916: 436560017: 0.00326818: 45670019: 46700020: 0.000067621: 36.0080022: 65.0023: 0.0000024: 789000025: 0.000326: 6576570027: 0.00050028: 5645600029: 0.0005630: 675670031: 67467032: 0.0065433: 43450034: 0.02045035: 876007636: 0.006540037: 568940038: 0.00060039: 593030040: 0.00770041: 492001042: 409033043: 0.075000044: 49030445745: 0.006070046: 479065047: 0.000627748: 5040346049: 0.006060050: 49040060051: 00000052: 58950053: 9640080054: 0.004504555: 35800050056: 0.0014357: 3212200058: 125800059: 0.00147460: 5120061: 18789062: 0.00002163: 9403410064: 20065354065: 0.00541966: 436260067: 0.00326868: 41270069: 42700070: 0.000067171: 17417072: 0.0021473: 43430074: 0.02041075: 823002176: 0.001240077: 218940078: 0.00020079: 193030080: 0.00320081: 192001082: 402033083: 0.012000084: 49030443285: 0.006030086: 00000087: 58910088: 9240080089: 0.004104590: 358000200Errors:104. Calculate the compound errors for x = s, dx = 1/T; y = T, dy = 1/k. as in physics:Forced vibration with damping: 105. Ty'' + my' + Ly = sin(Tx)Is there resonance? m = m35L = m10. Ty'' + Ly = sin(ωx)Find resonant ω.s = 19107012L = s Mod 10T = s Mod 100omega = Sqr(L / T)MsgBox omega as in physics:107. Find dot-product of tensor and vector LTameqa = m25e = m8L = m10m = m35q = m17T = m100Dim t(2, 2), v(2), r(2)s = 19107016a = s Mod 25e = s Mod 8L = s Mod 10m = s Mod 35q = s Mod 17tt = s Mod 100t(1, 1) = Lt(1, 2) = ttt(2, 1) = at(2, 2) = mv(1) = ev(2) = qr(1) = t(1, 1) * v(1) + t(1, 2) * v(2)r(2) = t(2, 1) * v(1) + t(2, 2) * v(2)MsgBox r(1)MsgBox r(2). Calculate π and hangover for T terms in each of the series.. Expand (a + b)L. L = m10. 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 11 9 36 84 126 126 84 36 9 1 110. Calculate c=0∞C(p,c)TxcExplain binomial series, combinations, Pascal triangle. series: 111. Expand sin(Tx) in the Taylor Series around 0. Take only terms 0, 1, 2, 3, 4.112. Calculate 327+1/T using linear approximation.113. Give truncation error for T terms of Taylor series for f(x).Fourier Series:114. Expand Tx in the Fourier Series. Take only terms 0, 1, 2, 3, 4.12*x*sin(x)/pi from –π to π12*x*sin(2x)/pi from –π to π12*x*sin(3x)/pi from –π to π12*x*sin(4x)/pi from –π to π calculus:115. Analyze normal distribution curve. Find its inflection point.π-∞xe-x2dxCalculate N(s).e^(-x^2)/sqrt(pi)from – infinity to 19107012. What is Cauchy distribution? is (π(1 + x2))-1 important? Find its inflection point.π-∞x1+x2-1dxCalculate C(s).((1+x^2)pi)^(-1)from – infinity to 19107012. If you toss T fair coins, then what is the most likely number of heads? Why?118. Give L’Hopital rule. = 0: Use L’Hopital rule to prove First Great Limit of Calculus: Limx→0sin?(x)x=m4 = 1: Limx→0xx=m4 = 2: Limx→1x2-3x+2x-1=m4 = 3: Limx→2x2-3x+2x-2=119. Explain: m6 = 0: Limitm6 = 1: Continuitym6 = 2: Derivativem6 = 3: Integralm6 = 4: Differential equationsm6 = 5: Series-Same as in physics: 120. Use differential to assess compound errors.m4 = 0: summ4 = 1: differencem4 = 2: productm4 = 3: quotient section: 121. Find volume and surface area of sphere with radius T.s = 19107012L = s Mod 10T = s Mod 100k = s Mod 10000E = s Mod 8q = s Mod 17A = s Mod 25d = (T - L) / 10Pi = 4 * Atn(1)R = Tvolume = 4 * Pi * R ^ 3 / 3SurfaceArea = 4 * Pi * R ^ 2MsgBox volumeMsgBox SurfaceArea coordinates:Do NOT change number 122.122. How many petals are there in R = sin(LA)? R = Radius. A = Angle. L = m10.. Give equation of T radius circumference in polar coordinates.124. Do integration by substitution sin(Tx).125. Calculate: a. 0Trxdxb. 0sixdxc. s-5sxdxd. k -5k xdxe.1/s1tanxdxf. 1/T1cotxdxrx = 1 if x is a rational number, rx = 0 if x is an irrational number.ix = 0 if x is a rational number, ix = 1 if x is an irrational number.. Determine the type of the partial differential equation. m2 = 0: -6Hxx + 7Hxt – 5Htt +675Hx – 34Ht + 54356 = 0m2 = 1: 39Hxx + 23Hxt – 305Htt - 6567Hx +56465Ht - 67467 = 0s = 19107012m2 = s Mod 2If m2 = 0 Then A = -6: B = 7: C = -5If m2 = 1 Then A = 39: B = 23: C = -305D = B ^ 2 - 4 * A * CIf D < 0 Then MsgBox "elliptic"If D = 0 Then MsgBox "parabolic"If D > 0 Then MsgBox "hyperbolic"Complex numbers: 127. Calculate: a. i-ab. i-Lc. imd. i1/(L+2) e. L+21 f. a – mi + Li – Tg. (a – mi)(Ti – L)h. (m – ai)/(Li – T) j. (k – ni)Lp. (a – mi)1/(L+2) q. inu. ikw. iLz. ian = sa = m25.m = m35.a.s = 19107012m2 = s Mod 2a = s Mod 25exponent = a Mod 4If exponent = 0 Then MsgBox "i^(-a) =1"If exponent = 1 Then MsgBox "i^(-a) =-i"If exponent = 2 Then MsgBox "i^(-a) =-1"If exponent = 3 Then MsgBox "i^(-a) =i"b.s = 19107012m2 = s Mod 2L = s Mod 10a = s Mod 25m = s Mod 35k = s Mod 10000n = sexponent = L Mod 4If exponent = 0 Then MsgBox "i^(-L) =1"If exponent = 1 Then MsgBox "i^(-L) =-i"If exponent = 2 Then MsgBox "i^(-L) =-1"If exponent = 3 Then MsgBox "i^(-L) =i"c.s = 19107012m2 = s Mod 2L = s Mod 10a = s Mod 25m = s Mod 35k = s Mod 10000n = sexponent = m Mod 4If exponent = 0 Then MsgBox "i^m =1"If exponent = 1 Then MsgBox "i^m =i"If exponent = 2 Then MsgBox "i^m =-1"If exponent = 3 Then MsgBox "i^m =-i"d.s = 19107012m2 = s Mod 2L = s Mod 10a = s Mod 25m = s Mod 35T = s Mod 100k = s Mod 10000n = sPi = 4 * Atn(1)x = 0y = 1R = Sqr(x ^ 2 + y ^ 2)alpha = Pi / 2For c = 0 To L + 1RealComponent = R ^ 1 / (L + 2) * Cos((alpha + 2 * c * Pi) / (L + 2))ImaginaryComponent = R ^ 1 / (L + 2) * Sin((alpha + 2 * c * Pi) / (L + 2))MsgBox "RealComponent"MsgBox "number"MsgBox cMsgBox RealComponentMsgBox "ImaginaryComponent"MsgBox "number"MsgBox cMsgBox ImaginaryComponentNext ce.s = 19107012m2 = s Mod 2L = s Mod 10a = s Mod 25m = s Mod 35T = s Mod 100k = s Mod 10000n = sPi = 4 * Atn(1)x = 1y = 0R = Sqr(x ^ 2 + y ^ 2)alpha = Atn(y / x)For c = 0 To L + 1RealComponent = R ^ 1 / (L + 2) * Cos((alpha + 2 * c * Pi) / (L + 2))ImaginaryComponent = R ^ 1 / (L + 2) * Sin((alpha + 2 * c * Pi) / (L + 2))MsgBox "RealComponent"MsgBox "number"MsgBox cMsgBox RealComponentMsgBox "ImaginaryComponent"MsgBox "number"MsgBox cMsgBox ImaginaryComponentNext cf.s = 19107012m2 = s Mod 2L = s Mod 10a = s Mod 25m = s Mod 35T = s Mod 100k = s Mod 10000n = sx1 = ay1 = -mx2 = -Ty2 = LRealComponent = x1 + x2ImaginaryComponent = y1 + y2MsgBox "RealComponent="MsgBox RealComponentMsgBox "ImaginaryComponent="MsgBox ImaginaryComponentg.s = 19107012m2 = s Mod 2L = s Mod 10a = s Mod 25m = s Mod 35T = s Mod 100k = s Mod 10000n = sx1 = ay1 = -mx2 = -Ly2 = TRealComponent = x1 * x2 - y1 * y2ImaginaryComponent = x1 * y2 + x2 * y1MsgBox "RealComponent="MsgBox RealComponentMsgBox "ImaginaryComponent="MsgBox ImaginaryComponenth.s = 19107012m2 = s Mod 2L = s Mod 10a = s Mod 25m = s Mod 35T = s Mod 100k = s Mod 10000n = sx1 = my1 = -ax2 = -Ty2 = LRealComponent = x1 * x2 + y1 * y2ImaginaryComponent = x2 ^ 2 + y2 ^ 2MsgBox "RealComponent="MsgBox RealComponentMsgBox "ImaginaryComponent="MsgBox ImaginaryComponentj.s = 19107012m2 = s Mod 2L = s Mod 10a = s Mod 25m = s Mod 35T = s Mod 100k = s Mod 10000n = sx = ky = -nR = Sqr(x ^ 2 + y ^ 2)alpha = Atn(y / x)RealComponent = R ^ L * Cos(L * alpha)ImaginaryComponent = R ^ L * Sin(L * alpha)MsgBox "RealComponent="MsgBox RealComponentMsgBox "ImaginaryComponent="MsgBox ImaginaryComponentp.s = 19107012m2 = s Mod 2L = s Mod 10a = s Mod 25m = s Mod 35T = s Mod 100k = s Mod 10000n = sPi = 4 * Atn(1)x = ay = -mR = Sqr(x ^ 2 + y ^ 2)alpha = Atn(y / x)For c = 0 To L + 1RealComponent = R ^ 1 / (L + 2) * Cos((alpha + 2 * c * Pi) / (L + 2))ImaginaryComponent = R ^ 1 / (L + 2) * Sin((alpha + 2 * c * Pi) / (L + 2))MsgBox "RealComponent"MsgBox "number"MsgBox cMsgBox RealComponentMsgBox "ImaginaryComponent"MsgBox "number"MsgBox cMsgBox ImaginaryComponentNext cq.s = 19107012m2 = s Mod 2L = s Mod 10a = s Mod 25k = s Mod 10000n = sexponent = n Mod 4If exponent = 0 Then MsgBox "i^n =1"If exponent = 1 Then MsgBox "i^n =i"If exponent = 2 Then MsgBox "i^n =-1"If exponent = 3 Then MsgBox "i^n =-i"u.s = 19107012m2 = s Mod 2L = s Mod 10a = s Mod 25k = s Mod 10000exponent = k Mod 4If exponent = 0 Then MsgBox "i^k =1"If exponent = 1 Then MsgBox "i^k =i"If exponent = 2 Then MsgBox "i^k =-1"If exponent = 3 Then MsgBox "i^k =-i"w.s = 19107012m2 = s Mod 2L = s Mod 10a = s Mod 25exponent = L Mod 4If exponent = 0 Then MsgBox "i^L =1"If exponent = 1 Then MsgBox "i^L =i"If exponent = 2 Then MsgBox "i^L =-1"If exponent = 3 Then MsgBox "i^L =-i"z.s = 19107012m2 = s Mod 2a = s Mod 25exponent = a Mod 4If exponent = 0 Then MsgBox "i^a =1"If exponent = 1 Then MsgBox "i^a =i"If exponent = 2 Then MsgBox "i^a =-1"If exponent = 3 Then MsgBox "i^a =-i"Unsolvable on paper integrals: 128. Calculate this integral: 1/T1sin?(x)xdxsin(x)/x from 1/12 to 1. Two computer companies make computers whose power increases: the first computers increase their power 2T% every two years and the second T% every year. Which computer power grows faster? Why?130. What gives the greater value 0.1T% decay in 2 years or 0.05T % every year? Why?131. Perform the errors analysis for the integral error bounds for x6 @[0, 1] taking 2T intervals.. Solve simultaneous equations.LTamxy=eqa = m25e = m8L = m10m = m35q = m17T = m100x = (em - Tq)/(Lm - aT)y = (Lq - ae)/(Lm - aT)s = 19107012a = s Mod 25e = s Mod 8L = s Mod 10m = s Mod 35q = s Mod 17T = s Mod 100x = (e * m - T * q) / (L * m - a * T)y = (L * q - a * e) / (L * m - a * T)MsgBox xMsgBox y. Give equations for geometrical transformations.m5 = 0: translationm5 = 1: stretchm5 = 2: enlargementm5 = 3: rotationm5 = 4: reflection-134. R is the radius-vector on a circumference. Calculate the dot-products and the cross-product. m3 = 0: R.R' = . . . m3 = 1: R'.R'' = . . . m3 = 2: R×R'' = . . . 135. Find relative change for instantaneous change ratio R = -1/T after d2 + 2 days. = 17108069T = s Mod 100L = s Mod 10d2 = (T - L) / 10R = -1 / Tx = d2 + 2MsgBox 1 - Exp(R * x)136. Solve the inequalities. m2 = 0: |k - Tx| < sm2 = 1: |-s + Lx| - |kx + T| < s. Calculatem3 = 0: curl(grad)m3 = 1: div(curl)m3 = 2: div(grad)?=i??x+ j??y+k??z, curl V = ?×V, div V =? . V, grad S = ? S138.m5 = 0: Explain Nabla operator.m5 = 1: Explain divergence.m5 = 2: Explain curl.m5 = 3: Explain gradient.m5 = 4: Explain Maxwell Equations.139. Find these dot-products and corresponding cross-products:m4 = 0: ij = m4 = 1: jj = m4 = 2: kj =m4 = 3: ki =140. Find these cross-products.m4 = 0: i×j = m4 = 1: j×j = m4 = 2: k×j =m4 = 3: k×i=-8 section:141. Predict extra class room for day L using Markov chain principle.L = 0: 209L = 1: 208L = 2: 203L = 3: 202L = 4: 201L = 5: 203L = 6: 203L = 7: 203L = 8: 204L = 9: 204Compare to the average and least squares approximation for L values. Dim room(10)room(0) = 209room(1) = 208room(2) = 203room(3) = 202room(4) = 201room(5) = 203room(6) = 203room(7) = 203room(8) = 204room(9) = 204s = 19107012L = s Mod 10If L < 1 Then MsgBox "no data for Markov chain prediction": GoTo 1MsgBox "Markov chain prediction is:"MsgBox room(L - 1)1 gfgh = uyiDim room(10)room(0) = 209room(1) = 208room(2) = 203room(3) = 202room(4) = 201room(5) = 203room(6) = 203room(7) = 203room(8) = 204room(9) = 204s = 19107012L = s Mod 10If L < 1 Then MsgBox "no data for average prediction": GoTo 1Sum = 0For c = 0 To L - 1Sum = Sum + room(c)Next cAverage = Round(Sum / L)MsgBox "average prediction is:"MsgBox Average1 gfgh = uyiDim x(10), y(10)n = 19107012k = n Mod 10000T = n Mod 100L = n Mod 10m = L - 1If L < 3 Then MsgBox "no data for linear regression prediction": GoTo 1MsgBox "linear regression prediction prediction is:"x(0) = 0x(1) = 1x(2) = 2x(3) = 3x(4) = 4x(5) = 5x(6) = 6x(7) = 7x(8) = 8x(9) = 9y(0) = 209y(1) = 208y(2) = 203y(3) = 202y(4) = 201y(5) = 203y(6) = 203y(7) = 203y(8) = 204y(9) = 204sx = 0For j = 0 To msx = sx + x(j)Next jsy = 0For j = 0 To msy = sy + y(j)Next jsxy = 0For j = 0 To msxy = sxy + x(j) * y(j)Next jsx2 = 0For j = 0 To msx2 = sx2 + x(j) ^ 2Next jg = (m * sxy - sx * sy) / (m * sx2 - sx ^ 2)i = (sy - g * sx) / mMsgBox Round(g * L + i)1 gfgh = uyiImproper integrals:142. Calculate a. 01dx1-x2 b. 01sinxxdx Use 2T nodes. numbers: 143. Find.a. (m – Ti)m3+3b. T+ima-Lic. m3+3T+mid. (T+im)(a-Li)e. (T+im)+(a-Li)f. (T+im)-(a-Li)L = m10.a = m25.m = m35.T = m100.a.s = 19107012m2 = s Mod 2L = s Mod 10a = s Mod 25m = s Mod 35T = s Mod 100k = s Mod 10000n = sm3 = s mod 3power = 3+m3x = my = -TR = Sqr(x ^ 2 + y ^ 2)alpha = Atn(y / x)RealComponent = R ^ power * Cos(power * alpha)ImaginaryComponent = R ^ power * Sin(power * alpha)MsgBox "RealComponent="MsgBox RealComponentMsgBox "ImaginaryComponent="MsgBox ImaginaryComponentb.s = 19107012m2 = s Mod 2L = s Mod 10a = s Mod 25m = s Mod 35T = s Mod 100k = s Mod 10000n = sx1 = Ty1 = mx2 = ay2 = -LRealComponent = (x1 * x2 + y1 * y2)/( x2 ^ 2 + y2 ^ 2)ImaginaryComponent = (x2*y1-x1*y2)/(x2 ^ 2 + y2 ^ 2)MsgBox "RealComponent="MsgBox RealComponentMsgBox "ImaginaryComponent="MsgBox ImaginaryComponentc.s = 19107012m2 = s Mod 2m3=s mod 3L = s Mod 10a = s Mod 25m = s Mod 35T = s Mod 100k = s Mod 10000n = sPi = 4 * Atn(1)RootPower = m3+3x = Ty = mR = Sqr(x ^ 2 + y ^ 2)alpha = Atn(y / x)For c = 0 To RootPower-1RealComponent = R ^ 1 / (RootPower) * Cos((alpha + 2 * c * Pi) / (RootPower))ImaginaryComponent = R ^ 1 / (RootPower) * Sin((alpha + 2 * c * Pi) / (RootPower))MsgBox "RealComponent"MsgBox "number"MsgBox cMsgBox RealComponentMsgBox "ImaginaryComponent"MsgBox "number"MsgBox cMsgBox ImaginaryComponentNext cd.s = 19107012m2 = s Mod 2L = s Mod 10a = s Mod 25m = s Mod 35T = s Mod 100k = s Mod 10000n = sx1 = Ty1 = mx2 = ay2 = -LRealComponent = x1 * x2 - y1 * y2ImaginaryComponent = x1 * y2 + x2 * y1MsgBox "RealComponent="MsgBox RealComponentMsgBox "ImaginaryComponent="MsgBox ImaginaryComponente.s = 19107012m2 = s Mod 2L = s Mod 10a = s Mod 25m = s Mod 35T = s Mod 100k = s Mod 10000n = sx1 = Ty1 = mx2 = ay2 = -LRealComponent = x1 + x2ImaginaryComponent = y1 + y2MsgBox "RealComponent="MsgBox RealComponentMsgBox "ImaginaryComponent="MsgBox ImaginaryComponentf.s = 19107012m2 = s Mod 2L = s Mod 10a = s Mod 25m = s Mod 35T = s Mod 100k = s Mod 10000n = sx1 = Ty1 = mx2 = ay2 = -LRealComponent = x1 - x2ImaginaryComponent = y1 - y2MsgBox "RealComponent="MsgBox RealComponentMsgBox "ImaginaryComponent="MsgBox ImaginaryComponent-144. Classify shape Tx2 + mxy + Ly2 = 1. s = 19107012L = s Mod 10m = s Mod 35T = s Mod 100A = TB = mC = LD = B ^ 2 - 4 * A * CIf D < 0 Then MsgBox "ellipse"If D = 0 Then MsgBox "parabola"If D > 0 Then MsgBox "hyperbola"-Same as in physics: 145. Solve the linear and non-linear real projectile problems for A = T degrees, V = T, R = 1/T. Linear:Going up:x'' + Rx' = 0y'' + Ry' = -gGoing down:x'' + Rx' = 0y'' - Ry' = -g up:x'' + R(x')2 = 0y'' + R(y')2 = -gGoing down:x'' + R(x')2 = 0y'' - R(y')2 = -gg = 10x(t)y(t)t = timeR = Dragx(0) = 0x'(0) = Vcos(A)y(0) = 0y'(0) = Vsin(A)Check if Vsin(A) > 1/T. Explain. How can you assess the solution for drag R if you have solution for case R = 0?*y%27%3D-10%2C+y%280%29%3D0%2C+y%27%280%29%3D1-Orthogonal polynomials:146. Expand sin(Tx) in Legendre polynomial series. Take only terms 0, 1, 2, 3, 4.(12x)/2 from -1 to 13*x*sin(12*x)/2 from -1 to 15*(3*x^2-1)*sin(12*x)/4 from -1 to 17(5*x^3-3x)*sin(12*x)/4 from -1 to 19(35*x^4-30x^2+3)*sin(12*x)/16 from -1 to 1. Give the orthogonal polynomials number L.. For what x is eLx = 0.5?s = 19107012L = s Mod 10x = Log(0.5) / LMsgBox x149. Find: a.1ssinxsinydxb.1scosxcosydy. Calculate the inner product.1/s1/ksinLxcosLxdxsin(12x)cos(12x) from 1/19107012 to 1/7012. How many petals are there in the flower R = cos(TA)?. Solve the differential equation Ty'' + my' + Ly = cos(kx), y(0) = 0, y'(0) = 1.*y%27%27%2B+32*y%27+%2B+11*y%3Dcos%289000*x%29%2C+y%280%29%3D0%2C+y%27%280%29%3D1153. Calculate correlation between s and date of birth.154. Plot parametric curves. m2 = 0: x = cos(t)sin(t), y = cos(t)m2 = 1: x = Sin(t), y = tCos(t). Give the series convergence tests.m3 = 0: ratiom3 = 1: rootm3 = 2: integral156. Give main coordinates.m3 = 0: polarm3 = 1: cylindricalm3 = 2: sphericalm4 = 0: 157. Show that dy = f'(x)dx.m4 = 1: 158. Prove that the lines y = Sx + I and y = gx + i are perpendicular if Sg = -1. m4 = 2: 159. Give equations of main quadric surfaces. = 3: 160. Why is integral more complex than derivative? -9 section: 161. Write equation of line perpendicular to y = Tx + L.162. Write equation of plane with normal (T, m, L). 163. Find perpendicular vector to (T, m, L).164. Find parallel vector to (T, m, L).165. Calculate triple product of (T, m, L), (a, s, k), (m7, m9, m17).166. Find multiple integral of F = xy = z, 0 < x < T, 0 < y < k.167. Give Jacobian for main coordinates.m3 = 0: polarm3 = 1: cylindricalm3 = 2: spherical168. Prove the Jacobian expression. m3 = 0: Polar coordinates.m3 = 1: Cylindrical coordinates.m3 = 2: Spherical coordinates. Same as in physics:169. Analyze latest events.Same as in physics:L = 0: 170. Play sociology game. Explore main scenarios. L = 1: 171. Give Tailor series of main functions. = 2: 172. What is conic section? as in physics: L = 3: 173. How do we avoid moto-bike accidents?Same as in physics: L = 4: 174. How do we protect ourselves in crowds, war, natural disaster, etc.?L = 5: 175. What is calculus of martial art?Same as in physics:L = 6: 176. How to fall with no hurt?Same as in physics:L = 7: 177. How can I protect my phone from being damaged? L = 8: 178. Give Jacobian for substitution, stretch, enlargement, translation, rotation, polar, cylindrical, spherical coordinates.Same as in physics:L = 9: 179. Forecast Jakarta flood.180. Give the best fit. section: Same as in physics: 181. What is your weight? 182. Plot 2 + m2 petals flower in polar coordinates.183. Give equation of circumference of T radius centered at (0, 0) in polar coordinates and in Cartesian coordinates.184. What is probability of randomly writing T letters? 185. Differentialm4 = 0: d(f+g) = m4 = 1: d(f-g) = m4 = 2: d(fg) = m4 = 3: d(f/g) = 186. Explain:m2 = 0: Orthogonal functionsm2 = 1: Orthogonal polynomialsL = 7: 187. Predict population of Indonesia in the year 2200.(x1+x2+x3)(y1+y2+y3)3x12+x22+x32-(x1+x2+x3)2i=y1+y2+y3-g(x1+x2+x3)3L = 8: 188. When will the population of Indonesia be 0? = 9: 189. Proveg=3x1y1+x2y2+x3y3-(x1+x2+x3)(y1+y2+y3)3x12+x22+x32-(x1+x2+x3)2i=y1+y2+y3-g(x1+x2+x3)3L = 0: 190. Discuss sum vs. integral. = 1: 191. Prove by induction. L = 2: 192. What is direct proportionality?L = 3: 193. Give main trigonometric equations.L = 4: 194. Give equations of main linear geometrical objects. Special functions: L = 5: 195. What is Zeta function? = 6: 196. Explain Bessel function. as in physics:L = 7: 197. When should be Christmas and New Year, according to modern astronomical data?Same as in physics: L = 8: 198. Analyze January 2020 events.en.wiki/Portal:Current_events/January_2020Same as in physics:L = 9: 199. Analyze 2020 Golden Globe Awards. as in physics: L = 0: 200. Explain Kazakhstan plane crash. is 11 January 2020. ................
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