Numerical Methods and Calculus

Question 31

The Newton-Raphson iteration X_{n + 1} = (X_n/2) + 3/(2X_n) can be used to solve the equation

• X² = 3
• X³ = 3
• X² = 2
• X³ = 2

Question 32

Which of the following statements is true?

• S > T
• S = T
• S < T and 2S > T
• 2S <= T

Question 33

A polynomial p(x) satisfies the following:

p(1) = p(3) = p(5) = 1 
p(2) = p(4) = -1 

The minimum degree of such a polynomial is

• 1
• 2
• 3
• 4

Question 34

[Tex] \\\\ \\lim_{x\\to \\infty } x^{\\frac{1}{x}} is [/Tex]

• ∞
• 0
• 1
• Not Defined

Question 35

• a
• b
• c
• d

Question 36

• 0.99
• 1
• 99
• 0.9

Question 37

[Tex] \\int_{\\frac{1}{\\pi}}^{\\frac{2}{\\pi}} cos(\\frac{1/x}{x^{2}})dx = ........... [/Tex]

• 0
• -1
• 1
• infinite

Question 38

Consider a function f(x) = 1 – |x| on –1 ≤ x ≤ 1. The value of x at which the function attains a maximum and the maximum value of the function are:

• 0, –1
• –1, 0
• 0, 1
• –1, 2

Question 39

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

1. f is continuous in [–1, 1]
2. f is not bounded in [–1, 1]
3. A is nonzero and finite 

• 2 only
• 3 only
• 2 and 3 only
• 1, 2 and 3

Question 40

[Tex] \\\\ The \\hspace{2 mm}value \\hspace{2 mm} of \\hspace{2 mm} \\lim_{x\\to\\infty }(1 + x^{2})e^{-x} is [/Tex]

• 0
• 1/2
• 1
• ∞