Question # 1

Suppose that f and g are differentiable function of x then d/dx[f][g]=

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[f'][g]-[f][g']/g²

[f'][g']

[f'][g]+[f][g']

According to Power -Rule of differentiation ,if f(x) =xⁿwhere n is a real number,then d/dx[xⁿ]

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x^n-1

nx^n-1

(n-1)x^n-1

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

The equation of the line of the form y-y₁=m(x-x₁) is known as

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Point Slope form

Two points form

Intercept form

Slop intersect form

Lim _x→_a^{f(x)=____ where f(x)=k?}

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k+2

K+1

k

The tan(x) is discontinuous at the point where

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Cos(x)=0

Sin(x)=0

Tan(x)=0

If the partial sum of series is finite then the series will be:

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Convergent

GIve no information

Not Sure

graph x =y²is symmetric about

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x axis

y axis

origin

Sigma notation is represent by

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M

N

Σ

If f(x)=e^-xat x=0 be the taylor series ,then which of the following is also true?

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Arithmetic Series

Maclaurin Series

Geometric Series

Harmonic Series

At which points two curves y=x²and y=x+6 intersect?

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x=0 and x=2

x=0 and x=3

x=2 and x=3

x=-2 and x=3

What is the sum of the following series?

1+2+3+----+n

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n+1/2

(n+1)(n+2)/2

n(n+2)/2

n(n+1)/2

d(tan x)/dx =___

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sec x

sec²x

cosec²x

cosec x

2/3 is known as

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even number

irrational number

natural number

rational 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)

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

If 2y-y=-3 then dy/dx ?

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2

-2

0

-3

An object is displaced 1m by a force of 1N then the work done

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2

1

0

if xy=4 they dy/dx ?

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-1/x²

4/x²

-4/x²

Average velocity of a body is V_ave

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d₁-d_o/ t₁- t_o

t₁- t_o/f(t₁₎- f(t_o)

_f(t₁₎- f(t_o)/t₁- t_o

None of these

How many critical points exist for a function f if f'(x)=(x-3)(x-2)

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0

1

3

2

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