Question # 1

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

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

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Divergent

Convergent

Give no information

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

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1

x

1/x

ln 1/x

The mean value of theorem states that " Let function f can be differentiable on (a,b) and continuous on [a,b] then there is no exist at least one point c in (a,b) where ______

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f'(c)=f(b)-f(a)/b-a

f(c)=f(b)-f(a)/b-a

f(c)=f(a)-f(b)/b-a

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

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2

1

0

if 2x-y=-3 they dy/dx=?

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2

-2

0

-3

For a function f ,let f'(x_n)=0 for some n Does the newton method for work for approximating the solution of f(x)=0

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yes

no

not sure

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

The tan(x) is discontinuous at the point where

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Cos(x)=0

Sin(x)=0

Tan(x)=0

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

lim x→0 sin2x/x____

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2

4

1

8

d/dx[cosec x]

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1/1+cos²x

-cos x/1-cos²x

1/1-cos²x

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)))

log_b1/c=_____?

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log_bc

1-log_bc

-log_bc

1+log_bc

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

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

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

If f(x)=3x⁸+2x+1 then f'x)

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3x⁷+2

24x⁷+2

3x⁷+23

y=x²/2

Let find the average rate of change of y with respect to x over the interval [3,4]

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25/2

7/2

25/14

7/14

d(tan x)/dx =___

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sec x

sec²x

cosec²x

cosec x

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

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