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QUESTION: 1

A function is given by f(t) = sin^{2}t + cos 2t. Which of the following is true?

Solution:

QUESTION: 2

Following are the values of a function y(x) : y(-1) = 5, y(0), y(1) as per Newton’s central difference scheme is:

Solution:

QUESTION: 3

Solution:

the squeeze theorem for this. Recall that sinx is only defined on −1≤sinx≤1. Therefore

QUESTION: 4

The function f(x) = |x+1| on the interval [-2, 0]

Solution:

f(x ) = x+ 1

f is continuous in [−2, 0]

but not differentiable at

x =−1 because we can draw

infinite number of tangents at x = −1

QUESTION: 5

If y=|x| for x<0 and y=x for x ≥ 0, then

Solution:

QUESTION: 6

What is the derivative of f(x) = |x| at x = 0?

Solution:

f( x ) = x .

At x = 0, we can draw infinitely many tangents at x=0.So limit does not exists.

QUESTION: 7

Solution:

= 1.0= 1

QUESTION: 8

Solution:

QUESTION: 9

The function Y=| 2-3x |

Solution:

QUESTION: 10

Solution:

QUESTION: 11

The function f(x) = x3 - 6x2 + 9x + 25 has

Solution:

QUESTION: 12

Solution:

QUESTION: 13

The value of the integral

Solution:

QUESTION: 14

The following plot shows a function y which varies linearly with x. The value of the integral I =

Solution:

Here the points (0,1) and (-1,0) are on the time

∴The equn of the line is

QUESTION: 15

The value of the integral

Solution:

QUESTION: 16

The length of the curve between x = 0 and x = 1 is

Solution:

Length of the wire

QUESTION: 17

Solution:

QUESTION: 18

A continuous-time system is described by y (t) = e ^{− x (t)} where y (t) is the output and x (t) is the input. y(t) is bounded.

Solution:

QUESTION: 19

Solution:

Since

QUESTION: 20

The value of the quantity P, where

Solution:

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