Question # 1

Let∫ be real valued function continuous in the interval (x,x₁)⊆ D∫ (the domain of∫),

then∱(x₁) -∱ (x)/x₁-x represents:

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Instantaneous rate

Average rate of change

Differential coefficient

None of these

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If ∱(x) = x^2/3then∱¹(x) at x = 8 equals:

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8

1/8

1/3

2/3

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1

0

cx

c

The derivative of 1/x^m is:

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x^m+1/ m

m(x)^m-1

(m-1) x^-m

m/x^m+1

If∱(x) = c then∱^{1 (x0 equals:}

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1

0

cx

c

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d/dx(x³ + 2x +3)=

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x²+ 2

3x + 2

3x²+ 5

3x2 + 2

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0

8

5

9

If y = xⁿthen dy/dx equals:

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nx

x^n-1

nx^n-1

n

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If∱(x) = x^-100the value of∱¹(1) is:

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100

-100

0

-101

If∱(x) = 1/x-2 then∱¹(0) equals:

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-1/4

-3/2

-1/2

1/5

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If y = (7x + 9)², then dy/dx equals:

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98x +126

14x

14x +18

14x+81

If∱(x) = x⁵ + x³ + x the value of∱¹(1) is:

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0

8

5

9

If y = 3 x + 2cos x, then dy/dx =

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3-2 sin x

3-t sin x

3x² - 2sin x

3(1-4 sin x)

d / dx (cot x) =

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Sec x tan x

-csc² x

Sec² x

1/cot² x

d/dx [tan² x]

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2tan x sec² x

2tan x sec x

2 cot x tan x

2sec² x cos² x

Differentiation of sin x w.r.t. cot x is:

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-sin² x sec x

-cos x sin² x

-cos² x tan x

-sin² x

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If∱(x) = 2x³ + 1 then∱¹(0) =

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0

1

6

None of these

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∱(x) = ax²-3x -5, and∱¹(2) = 9, a is equal to

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2

3

-2

4

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-2x

x^-3

-2x³

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d/dx (cos x²) =

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-2x cos x

-2x sin x²

-2x tan x

-2x sec² x

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