The solution of differential equation y'' + 3y' + 2y = 0 is of the form

(a) Determine the number of divisors of 600.
(b) Compute without using power series expansion

Consider the functions

I. e^-x
II. x²-sin x
III. √(x³+1)

Which of the above functions is/are increasing everywhere in [0,1]?

The formula used to compute an approximation for the second derivative of a function f at a point X₀ is

What is the maximum value of the function f(x) = 2x² - 2x + 6 in the interval [0,2]?

Consider the function y = |x| in the interval [-1,1]. In this interval, the function is

(a) Find the points of local maxima and minima, if any, of the following function defined in 0 ≤ x ≤ 6.

  x3 - 6x + 9x - 15 

(b) Integrate

Which of the following statements is true?

Backward Euler method for solving the differential equation dy/dx = f(x,y) is specified by, (choose one of the following).

The differential equation
d²y/dx² + dy/dx + siny = 0 is:

Fourier series of the periodic function (period 2π) defined by

But putting x = π, we get the sum of the series.

Which of the following improper integrals is (are) convergent?

The radius of convergence of the power series

The value of the double integral is

The differential equation yⁿ + y = 0 is subjected to the boundary conditions.

    y (0) = 0        y(λ) = 0         

In order that the equation has non-trivial solution(s), the general value of λ is __________

If f(1) = 2, f(2) = 4 and f(4) = 16, what is the value of f(3) using Lagrange’s interpolation formula?

Consider the following iterative root finding methods and convergence properties:

Iterative root finding          Convergence properties methods 
(Q) False Position                (I) Order of convergence = 1.62 
(R) Newton Raphson               (II) Order of convergence = 2 
(S) Secant                      (III) Order of convergence = 1 
                                      with guarantee of convergence 
(T) Successive Approximation     (IV) Order of convergence = 1 
                                      with no guarantee of convergence 

If the trapezoidal method is used to evaluate the integral obtained ₀∫¹x²dx ,then the value obtained

What is the value of

The following definite integral evaluates to

If f(x) is defined as follows, what is the minimum value of f(x) for x∊(0,2] ?

If f(x) = Rsin(πx/2) + S, f'(1/2) = √2 and , then the constants R and S are, respectively.

Let f(x) = x ^-(1/3) and A denote the area of the region bounded bu f(x) and the X-axis, when x varies from -1 to 1. Which of the following statements is/are TRUE?

I) f is continuous in [-1,1]
II) f is not bounded in [-1,1]
III) A is nonzero and finite

If g(x) = 1 - x and h(x) , then is:

Let f(x) be a polynomial and g(x) = f'(x) be its derivative. If the degree of (f(x) + f(-x)) is 10, then the degree of (g(x) - g(-x)) is __________.