Question # 1

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)))

A line is called a tangent line to the circle if it meets the circle at precisely.....

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one point

two point

infinite points

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

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

The PYTHAGORAS theorem describe the relationship between the sides of

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Right angle triangle

Isoceleous Triangle

Equilateral traingle

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

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1

-1

1/(1-x)²

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

If f and g are continuous function on an interval [a,b] f(x)>=g(x) for a<=x<=b and ,then area is bounded by the lines parallel to :

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X-axis

Y axis

Both x and y axis

log_ba^r=____?

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a log_br

rlog_ba

log_ba/log_br

If a function has an extreme value (either a maximum or a minimum ) on an open interval (a,b) then the extreme value occurs at ____ of f

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First point

Mid point

Critical Point

End Point

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

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0

1

3

2

if x²+y²=9 then dy/dx=?

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x/y

-x/y

-y/x

a function f is ___ on a closed interval [a,b] ,then f has both a maximum and minimum value on [a,b]

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Continuous

Discontinuous

None of these

Chain rule is a rule for differentiating ______ of functions

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Product

Sum

Composition

Difference

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 a quantity y depends on another quantity x in such a way that each value of x determines exactly one value of y ,we say that y is ____ of x

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relation

function

not a function

not a relation

log_b1/c=_____?

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log_bc

1-log_bc

-log_bc

1+log_bc

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

Sigma notation is represent by

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M

N

Σ

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

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Non increasing

non decreasing

increasing

decreasing

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

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