Question # 1

Which of the following is true for the sequence {n}∞ n=0?

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Non increasing

non decreasing

increasing

decreasing

if x²+y²=9 then dy/dx=?

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x/y

-x/y

-y/x

30^o

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π/3

π/4

π/6

For a sequence {a_n} if the difference between successive terms a_n+1-a_n<=0 then the sequence is known as

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increasing

decreasing

non decreasing

non increasing

Let x_obe the critical point of the function f,those critical point for which f'(x_o)=0 are called _______ of

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Local points

End points

Stationary points

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']

Which of the following are first two terms for the taylor series of f(x)=e^-xat x=0?

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1+(1)(x-0)

1+(-1)(x-0)

1+(-1)(x+0)

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)

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

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 xy=4 they dy/dx ?

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-1/x²

4/x²

-4/x²

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

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2

1

0

d(tan x)/dx =___

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sec x

sec²x

cosec²x

cosec x

Which operation can not be applied on the function?

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Subtraction

Cross Product

Addition

Composition

For a sequence {a_n}if the ration of successive terms a_n+1/ a_n>1 then the sequence is known as

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Increasing

Decreasing

Non Increasing

Non decreasing

Lim _x→₀sinx/x

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1

-1

0

2

π is a _____ number

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rational

irrational

natural

integer

______ is the special case of Taylor's Theorem

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Roll's theorem

Picard Method

Integration

log_ba^r=____?

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a log_br

rlog_ba

log_ba/log_br

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

tan x is continuous everywhere except at points

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+- kπ/2 (k=1,3,5....)

+- kπ/2 (k=2,4,6....)

Not Sure

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