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) = c then∱^{1 (x0 equals:}

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1

0

cx

c

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100

-100

0

-101

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1

0

cx

c

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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)

If c is a constant, then d/dx (c) =

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0

c

cx

1

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If y=x^mthen dy/dx equals:

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mx

x/m

mx^m-1

xm^m-1

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x²+ 2

3x + 2

3x²+ 5

3x²+ 2

if x∈ D∱ and∱¹^{(x) exists, then}∱ is said to be

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zero at x

Differentiable at x

Continuous at x

None of these

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None of these

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

If f(x) = c then∱¹(x) equals:

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1

0

cx

c

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-2x

x^-3

-2x³

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If∱(x) = 1/x-2 then∱¹(0) equals:

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-1/4

-3/2

-1/2

1/5

if y=x²then dy/dx equals:

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2x

x/2

2x³

x³/2

If 3x + 4y +7 = 0 , then dy / dx =

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-1/2

-4/3

7/2

-3/4

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

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8

1/8

1/3

2/3

If∱(x) = x^-100the value of∱¹(1) is:

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100

-100

0

-101

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x^n-1

If x² + y² = 1, then dy/dx

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y/x

-x/y

1/x

None of these

If x = at² and y = 2at then dy/dx =

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2a/y

y/2a

-a/2y

-2y/a

d/dx (cos x²) =

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-2x cos x

-2x sin x²

-2x tan x

-2x sec² x

If y = xⁿthen dy/dx equals:

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nx

x^n-1

nx^n-1

n

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0

8

5

9

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