Mathematics - II
Attempt any Six question
2. Write expansions for log(1+x) and ex and use the expansion ex to prove
3. Find Derivative of using defination.
4. Show that the rectangle of largest possible area for a given perimeter 'P' is a square.
5. Evaluate the integral,
6. Solve the differential equation
7. Evaluate the limit
8. Using Newton Raphson's Method to find the square root fo 153 correc to three places of decimals.
Attempt any Two question
9. Using simplex method to find the optimal solution of the following linear programming problem.
maximize, z = 2x1 + 12x2 + 8x3
2x1 - 2x2 + x3 ≤ 100
x1 - 2x2 + 5x3 ≤ 80
10x1 + 5x2 + 4x3 ≤ 80,
x1, x2, x3 ≥ 0
10. a) State Mean value Theoren and interpret it geometrically
b) Find the intervals in which the function f(x) = x3 - 3x2 + 5 concave upwards and concave downward.
11. a) Find the area bounded by the parabola y2 = 4x and y axis between the point y = 0 to y = 2.
b) Solve the differential equation