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UTS in calculus made by Michael Marchenko in October of 2019.Edited at 1pm 16.10.2019.s is your student number. Write your student number: s = ___________________Write your name ___________________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. 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 2.1. Describe your project. Choose topic and write research paper about it.2. Solve Zimmermann problem,3. 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: 4. When does limit exist? = 1: 5. List indeterminate forms. = 1: 6. What the properties of the limit? (times constant, sum, product, quotient)m2 = 0: 7. Give the main methods for calculating limits. 8. 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: 9. Give the properties of derivative: times constant, sum, product, quotient. m2 = 0: 10. Prove expression for derivative of x2 using limit. 11. 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) is when derivative > 0.decrease is when derivative < 0.13. Concave or convex:m4 = 0: x3m4 = 1: -x3m4 = 2: cos(x)m4 = 3: sin(x) up is is when second derivative < 0.concave up is is when second derivative > 0.14. Find inflection point:m4 = 0: x3m4 = 1: -x3m4 = 2: cos(x)m4 = 3: sin(x) is when second derivative = 0.15. 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. Use derivative to find min and Max.16. Calculate (1+1/T)T. close is this to e?17. Solve number puzzle for 3 + m8 digits. . Hack password. answered this on 2 October 2019.19. Limx→pfx = L. f(x) = Tx + k. For any ε find δ, using ε – δ definition of the limit.20. Find the discriminant of the elliptic curve y2 = x3 + Lx + T.Here L = m10. is for cryptography and cryptoanalysis.21. Find linear least-square approximation for your dataset. (2, m2), (3, m3), (4, m4) derivative to find min.22. 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.. Calculate derivative, using Chain Rule for sin(Tx)27. Find partial derivatives. m2 = 0: x + ym2 = 1: xy28. Calculate total derivative.m2 = 0: x + ym2 = 1: xy29. Find implicit function derivative. Lx2 + Ty2 – k = 030. Calculate inverse function derivative y = Tx + L.31. Analyze y = Tx + L. Find gradient, intercept, derivative, parallel line, perpendicular line. 32. Explainm8 = 0: composite functionm8 = 1: inverse functionm8 = 2: implicit functionm8 = 3: algebraic functionm8 = 4: transcendental functionm8 = 5: special functionm8 = 6: exponential functionm8 = 7: logarithmic function33. Explainm6 = 0: natural numberm6 = 1: integerm6 = 2: rational numberm6 = 3: irrational numberm6 = 4: real numberm6 = 5: complex number34. Integrate.xTdxsinTx dx01xTdx01sinTxdx. eTxdx36. 01eTxdx ................
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