Question # 1

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

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1

x

1/x

ln 1/x

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

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Convergent

GIve no information

Not Sure

30^o

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π/3

π/4

π/6

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']

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

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

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

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2

-2

0

If the geometric series a+ar+ar²+ar³.......+ar^{k-1 which of the following is true for the given series}

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converges

Diverges

Give no information

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

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[g][f'] - [f][g']/g²

[g'][f] - [f'][g]/g²

[g'][f] - [f'][g]/f²

h(x)=1/(x-2)(x-4) domain of the function is

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(-∞,2)U (2,4)U (4,+∞)

(-∞,2)U (2,4)U (4,∞)

All are incorrect

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

set{...-4,-3 ,-2,-1,0,1,2,3,4} is known as the set of

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natural number

Integer

whole number

The graph x=y²is symmetric about ___ axis

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X -axis

Y-axis

origin

Which operation could not be applied on the function?

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Cross Product

Sum

Division

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

log_ba^r=____?

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alog_br

r log_ba

log_ba /log_br

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 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

log_bac=_________

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log_ba + log_bc

log_ba - log_bc

log_ba/log_bc

log_ba * log_bc

(x²-4)/(x-2) Natural domain is

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(-∞,2)U (2,+∞)

(-∞,2)

(-∞,0)

None of these

______ is the special case for the Taylor's theorem

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Roll's Theorem

Picard's Method

Integration

Maclaurin Theorem

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