Question # 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

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

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Divergent

Convergent

Give no information

Lim _x→_a^{f(x)=____ where f(x)=k?}

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k+2

K+1

k

Chain rule is a rule for differentiating ______ of functions

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Product

Sum

Composition

Difference

(x²-4)/(x-2) Natural domain is

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(-∞,2)U (2,+∞)

(-∞,2)

(-∞,0)

None of these

If f is a continuous function such that lim_x_→+_∞=+∞ andlim_x_→+_∞=+∞ the f has on

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maximum value but no minimum

minimum value but not maximum

both maximum and minimum value

Function f is differentiable function if it is differentiable on the interval

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(-∞,∞)

(a,∞) where a is any negative integer

(0,∞)

None of these

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)

Center and radius of the circle is (x+5)²+(y-3)²=16 is

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(-5,3),4

(5,-3),16

(5,-3),4

None of these

Tan(x) is continuous every where except at points

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+- kπ/2 where k=(1,3,5.....)

+- kπ/2 where k=(2,4,6.....)

+- kπ/2 where k=(1,2,3,4,5,6.....)

Let y=(x³+2x)³⁷ Let Which of the following is correct?

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dy/dx=(37)(x³+2x)³⁶

dy/dx=(111x²)(x³+2x)³⁶

dy/dx=(111x²+74)(x³+2x)³⁶

If there is some function F such that d/dx[F(x)]=f(x) then antiderivatives of f(x) are F(x)+C .What does C represent?

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Polynomial

Constant

Dependent variable

Independent variable

If x>0 then d/dx[lnx]=_______

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1

x

1/x

ln 1/x

______ is the special case of Taylor's Theorem

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Roll's theorem

Picard Method

Integration

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

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0

1

3

2

The graph x=y²is symmetric about ___ axis

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X -axis

Y-axis

origin

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']

d(tan x)/dx =___

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sec x

sec²x

cosec²x

cosec x

The equation (x+4)²+(y+1)²=6 represent a circle having center at____ and radius

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(-4,1),undertoot 6

(-4,-11),undertoot 6

None of these

Suppose that f and g are differentiable function of f x then d/dx(f)(g)=

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[f'][g]-[f][g']/g²

[f'][g']

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

{1/2ⁿ}ⁿ1 represent the sequence

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-1/2,-1/4,-1/8

1/2,1/4,1/7=8

0,1,1/2,1/4

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