Calculus17.weebly.com
UAS in calculus made by Michael Marchenko in November of 2019.Edited at 5am 30.11.2019.s is your student number.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.Main questions:1.102. How many significant figures are there in your T number?Errors:2.104. Calculate the compound errors for x = s, dx = 1/T; y = T, dy = 1/k. pluses for errors. Same as in physics:Forced vibration with damping: 3.105. 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:5.107. 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 . Calculate c=0∞C(p,c)TxcExplain binomial series, combinations, Pascal triangle. series: 9.111. Expand sin(Tx) in the Taylor Series around 0. Take only terms 0, 1, 2, 3, 4.10.112. Calculate 327+1/T using linear approximation.11.113. Give truncation error for T terms of Taylor series for f(x).Fourier Series:12.114. Expand Tx in the Fourier Series. Take only terms 0, 1, 2, 3, 4.Statistical calculus:13.115. 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?16.118. 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=17.7. Describe your project. 18.122. How many petals are there in R = sin(LA)? R = Radius. A = Angle. L = m10.. 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. Give equation of T radius circumference in polar coordinates.21.124. Do integration by substitution sin(Tx).22.125. 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 = 024.127. 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.Unsolvable on paper integrals: 25.128. Calculate this integral: 1/T1sin?(x)xdx26.129. 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?27.130. What gives the greater value 0.1T% decay in 2 years or 0.05T % every year? Why?28.131. 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. 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)-Additional questions: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?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?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: 358000200119. Explain: m6 = 0: Limitm6 = 1: Continuitym6 = 2: Derivativem6 = 3: Integralm6 = 4: Differential equationsm6 = 5: SeriesSame as in physics: 120. Use differential to assess compound errors.m4 = 0: summ4 = 1: differencem4 = 2: productm4 = 3: quotient section: 133. Give equations for geometrical transformations.m5 = 0: translationm5 = 1: stretchm5 = 2: enlargementm5 = 3: rotationm5 = 4: reflection134. 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'' = . . . 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= ................
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