If f(1)=1,f^(prime)(1)=2, then write the...

If `f(1)=1,f^(prime)(1)=2,` then write the value of `(lim)_(x->1)(sqrt(f(x))-1)/(sqrt(x)-1)`

A

1

B

2

C

3

D

4

Text Solution

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Knowledge Check

If f(1)=1,f'(1)=2 then underset(x to 1)lim""(sqrt(f(x))-1)/(sqrt(x)-1) is

A

2

B

4

C

1

D

`(1)/(2)`

Let f(x)=(1)/(sqrt(18-x^(2))) What is the value of lim_(xto3) (\f(x)-f(3))/(x-3) ?

A

0

B

`-(1)/(9)`

C

`(1)/(3)`

D

`(1)/(9)`

If int(x(x-1))/((x^(2)+1)(x+1)sqrt(x^(3)+x^(2)+x))dx =(1)/(2)log_(e)|(sqrt(f(x))-1)/(sqrt(f(x))+1)|-tan^(-1)sqrt(f(x))+C, then The value of lim_(x to oo) tan^(-1)sqrt(f(x)) is

A

`pi//2`

B

`pi//4`

C

`pi`

D

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