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ā‡± Quiz about Numerical Methods and Calculus

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Question 1

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

  • One, at Ļ€/2

  • One, at 3Ļ€/2

  • Two, at Ļ€/2 and 3Ļ€/2

  • Two, at Ļ€/4 and 3Ļ€/2

Question 2

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

  • 7

  • 5

  • 3

  • 1

Question 3

Function f is known at the following points: 

šŸ‘ gatecs201310



  • 9.003 

  • 9.017 

  • 8.983 

  • 9.045

Question 4

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 ā‰  3

Question 5

Given i=āˆš-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]?

  • -i

  • 2

  • 0

  • i

Question 6

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

  • 3.607

  • 3.667

  • 3.676

  • 3.575

Question 7

What is the value of Limnā†’āˆž(1-1/n)2n ?

  • 1

  • e-2

  • e-1/2

  • 0

Question 8

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?

  • 12

  • 10

  • 6

  • 5

Question 9

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

  • 0

  • 1

  • ln 2

  • 1/2 ln 2

Question 10

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 āˆ© B is

  • [-1, 0]

  • [-1, 0)

  • [-āˆž, 0]

  • [-āˆž,1]

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