Question # 1

______ is the special case for the Taylor's theorem

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Roll's Theorem

Picard's Method

Integration

Maclaurin Theorem

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)

Consider a function h(x) and a constant c then d/dx{(c){h(x)}}

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0

d/dx((h(x)))

d/dx((h(cx)))

cd/dx((h(x)))

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

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

The set {x:a<=x<=b} can be written in the form of interval ?

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(a,b)

(a.b)

[a,b]

If f(x)=3x⁸+2x+1 then f'x)

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3x⁷+2

24x⁷+2

3x⁷+23

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)

If y=1/1-x the dy/dx=____?

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-1

1

1/(1-x)²

if x²+y²=9 then dy/dx=?

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x/y

-x/y

-y/x

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

Which operation could not be applied on the function?

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Cross Product

Sum

Division

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

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

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Non increasing

non decreasing

increasing

decreasing

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

2/3 is known as

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even number

irrational number

natural number

rational number

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

The lim x→a f(x)=___ where f(x)=k

The k is constant

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K+1

K+2

k

Suppose that we apply newton method to approximate the real solution of the equation x³-2x²-1=0 if we start at x₁=2,then which of the following is value of x₂?

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6

2.25

0

2

y=1/1-x dy/dx if then

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1

-1

1/(1-x)²

log_b1/t =________

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log_bt

1-log_bt

1+log_bt

-log_bt

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