Numerical Methods and Calculus (original) (raw)

Consider the function f(x) = sin(x) in the interval [π/4, 7π/4]. The number and location(s) of the local minima of this function are

The bisection method is applied to compute a zero of the function f(x) = x4 – x3 – x2 – 4 in the
interval [1,9]. The method converges to a solution after ––––– iterations

Function f is known at the following points:

Which one of the following functions is continuous at x = 3?

• [Tex]f(x)=\left\{\begin{array}{lll}2, & \text { if } & x=3 \\ x-1, & \text { if } & x>3 \\ \frac{x+3}{3}, & \text { if } & x<3\end{array}\right.[/Tex]
• [Tex]f(x)=\left\{\begin{array}{lll}4, & \text { if } & x=3 \\ 8-x & \text { if } & x \neq 3\end{array}\right.[/Tex]
• [Tex]f(x)=\left\{\begin{array}{lll}x+3, & \text { if } & x \leq 3 \\ x-4, & \text { if } & x>3\end{array}\right.[/Tex]
• [Tex]f(x)=\frac{1}{x^3-27}, [/Tex]if x ≠ 3

Given i=√-1, what will be the evaluation of the integral [Tex]\int_{0}^{\pi/2} \frac{\cos x + i\sin x}{\cos x - i\sin x} dx[/Tex]?

Newton-Raphson method is used to compute a root of the equation x2-13=0 with 3.5 as the initial value. The approximation after one iteration is

What is the value of Limn→∞(1-1/n)2n ?

Two alternative packages A and B are available for processing a database having 10k records. Package A requires 0.0001n2 time units and package B requires 10nlog10n time units to process n records. What is the smallest value of k for which package B will be preferred over A?

[Tex]\int_{0}^{\pi/4} \frac{1 - \tan x}{1 + \tan x} dx[/Tex] is equivalent to

Let f(x) = log|x| and g(x) = sin x . If A is the range of f(g(x)) and B is the range of g(f(x)) then A ∩ B is

There are 93 questions to complete.

Take a part in the ongoing discussion