Question # 1

Let f(x ) is the function such that as x approaches a real number ,either from left or right hand side ,the function value increase or decrease unboundedly then lim f(x)

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Exist

Does not exist

Not Sure

If a function g is differentiable at a point x and function f is differentiable at a point g(x),then the __ is differentiable a point x.

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Composition (fog)

Quotient f/g

product f.g

Sum (f+g)

The power rule d/dx[xⁿ]=nx^n-1holds if n is

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an integer

a rational number

an irrational number

all of the above

set{...-4,-3 ,-2,-1,0,1,2,3,4} is known as the set of

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natural number

Integer

whole number

A function f is called antiderivative of a function on a given interval if ______ =f(x),for all x in that interval

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F'(x)

F(x)

f(x)

f''(x)

y=f(x) then the average rate of change of y with with respect to x over the interval [x_o,x₁] is the _______ joining the points (x_{o ,f(}x_o₎) and (x₁f(x₁)) on the graph of f

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Slope of the secant line

Slope of the tangent line

Secent line

none of these

In alternating series test ,which one of the following condition must be satisfied

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lim k→∞ a_k=1

a₁>a₂>a_{3...............>a}k

a₁<a₂<a_{3...............<a}k

If f is a twice differentiable function at stationary point x_oan f'(x_o) >0 then f has relative _______ At x_o

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Minima

Maxima

None of these

d(sec x)/dx=?

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sec x tan x

sec x tan y

cosec x cot x

Which of the following is the spring constant k if a spring constant whose natural length is 2m exerts a force of 3N when started 1m beyond its natural legth?

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3 x

3 N/m

2 m

lim x→0 sin2x/x____

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2

4

1

8

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