BSc CS Sem 2 2022 2023 April 2023 Calculus Question Paper - Mumbai University | munotes

Questions asked in this paper

1. Q1 If f(x) = 69-24x-9 x3, find the intervals on which the function f(x) is increasing and 2.For what values of x the curve y = 3 x2- 2 x? is concave downwards and when it is concave 3.Find the asymptotes of the function y = 4.Find the intervals on which function f is increasing or decreasing, where f(x) = +5 5.Divide the number 25 into two parts such that the square of one part is multiplied with the cube of the other part is maximum 6.Determine the absolute extrema for the function f(x) = sin x —x cos x
2. Q2 Solve Evaluate the following.(Any 4 ) {Marks : 15] 1.Evaluate dx 2.Evaluate J dx 3.Find area between the graph of cos x and on[0, 7/4 ]
   • A.Find the arc length of the curve y = forx 0, 4] 5.Solve ay = by using substitution y =v x 6.Evaluate dx for n = 6 by Simpson’s rule
   • q.3.Solve the following.(Any 4) {Marks : 15]
3. Q1 Find the directional derivative of f(x,y) = 4y at u= (2,3) along
4. Q2 Find the maximum and minimum rates of change in f at u if f( x,y,z)=x2+ and u = ( 1,2,3) Also state their direction 3.Find the linearization of function f(x, =x? +xy + at the point (1, 2) 4.Find the equation of tangent and normal for the function x? + —2 x 25 =O at the
5. Q5 The function f =x? - Find all local maximum and local minimum
6. Q6 For the function f (x, +cosxsiny
7. Q4 Solve the following.(Any 5 ) {Marks : 15] 1.Show that, the function f(x) = 10 + 12x + 3 x? is always decreasing 2.Divide the number 100 into two parts such that their product is maximum 5.For the function f( x, y ) = cos 2y.Hence find V f ( 0,5) 6.For the function f( x, y 7 x*y3-5 whether = fyx or not 7.Find implicit differentiation of the function y = y y—2 at (0,2)

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