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Find the differential d y and evaluate for the given values of x and y = (x^{2}+5)^{3}, x = 1 ,d x = 0.05

(A)

8.8

(B)

9.8

(C)

10.8

(D)

none of these

Question-2

The curve y^{2}(x-2) = x^{2} (1+x) has

(A)

An asymptote parallel to x- axis

(B)

An asymptote parallel to y -axis

(C)

An asymptote parallel to both axis

(D)

No asymptotes

Question-3

The differential of x^{5} is

(A)

5 x^{3} d x

(B)

4 x^{4} d x

(C)

5 x^{5}d x

(D)

5 x^{4}d x

Question-4

The differential of y = is

(A)

(B)

(C)

(D)

Question-5

The differential of sin 2 x is

(A)

2 cos x d x

(B)

2 sin 2 x d x

(C)

2 cos 2 x d x

(D)

none of these

Question-6

If x = r cos θ, y = r sinθ then is equal to

(A)

sec θ

(B)

sin θ

(C)

cos θ

(D)

cosec θ

Question-7

The differential of x tan x = y is

(A)

(x sec^{2} x + tan x)dx

(B)

(x^{3 }sec^{2 }x + tan x ) dx

(C)

(x tan^{2} x+ sec x )dx

(D)

none of these

Question-8

If u = , then is equal to

(A)

(B)

u

(C)

(D)

-u

Question-9

Find the differential d y and evaluate d y for the given values of x and d x y = x^{4}- 3 x^{2}+ x - 1, x = 2, d x = 0.1

(A)

0.1

(B)

1.1

(C)

2.1

(D)

3.1

Question-10

The time of swing T of a pendulam is given by T= k where k is a constant. Determine the percentage error in the time of swing if the length of the pendulum 1 changes from 32.1 cm to 32.0 cm

(A)

0.146

(B)

0.156

(C)

-0.146

(D)

-0.156

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