BSc CS Sem 2 BSc CS Semester 2 (2018 2019) Apr 2019 CALCULUS Question Paper - Mumbai University | munotes

Questions asked in this paper

• 2) Figures to the right indicate marks

1. Q3 Illustrations, in-depth answers and diagrams will be appreciated
2. Q4 Mixing of sub-questions is not allowed
3. Q1 Attempt All (Each of 5Marks) (15M)
   • (a) Select correct answer from the following:
4. Q1 In which of the following method, we approximate the curve of solution by the tangent in each interval
   • a) Simpson’s Method
   • b) Euler’s method
   • c) method
   • d) None of the above 2)f 1/(9x? +25) dx=
5. Q3 A function is said to be invertible if and only if it is
6. Q4 lim 7/2x =
7. Q5 If f(x, y)= y3+1 then f,(x, y) is
   • a)3x? b) 3xy c) d) None
   • (b) Fill in the blanks: The derivative of ex is
8. Q3 Unit vector of is
9. Q4 +3) dx=
10. Q5 The rate of change of one variable with respect to another is called
    • Q.P. Code: 31173
    • (c) Answer the following in one line
11. Q1 Define Tangent Plane
12. Q2 Define Critical Point
13. Q3 Define the term Definite Integral
14. Q5 Linearization of a function
15. Q2 Attempt the following (Any THREE) (15M)
    • (a) Show that lim
    • (b) Discuss the continuity of the function x?
    • (c) Show that the function f(x) = x3- 9x? +30x + 7 is always increasing
    • (d) Find the relative extrema of f(x) = using both first and second
    • (e) Using Newton’s method find the approximate root for the equation
    • (f) Divide 100 into two parts such that sum of their square is minimum
16. Q3 Attempt the following (Any THREE) (15M)
    • (a) Evaluate dx
    • (b) Evaluate dx
    • (c) Estimate fox? dx using simpson’s rule and n= 4
    • (d) Solve the differential equation
    • (e) Solve dy/dx = 1 —y; y(0) =0, find y(0.1) and y(0.3) using Euler’s method. Taking
    • (f) Solve the differential equation
17. Q4 Attempt the following (Any THREE) 15 marks
    • (a) Show that f(x, y) = 2x? +3xy is continuous at (2, 3)
    • (b) Find the second order derivatives of f(x,y)=x*y? + x*y
    • (c) If x=t? and y=t? Use chain rule to find <
    • (d) Find the directional derivative of f(x, y)=x? at the point (-2, -3) in the direction of the vector a=
    • (e) Find the gradient vector of f(x, y) if f(x, y) = 10 — 8x? — Evaluate it at
    • (f) Find the equation for the tangent plane and parametric equations for normal line to the surface z=x?y at the point (2, 1, 4)
    • Q.P. Code: 31173
18. Q5 Attempt the following (Any THREE) 15 marks
    • (a) Locate all relative extrema and saddle points of
    • (b) Solve the differential equation
    • (c) Draw the graph of y= 4 — 3x? + x? and find the intervals on which the function y is increasing and decreasing(draw the graph on the answer sheet itself)
    • (d) the asymptotes of the function y=
    • (e) Solve the differential equation

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