Home
Class 12
MATHS
If f(x) is continuous in [0,1] and f(1/...

If f(x) is continuous in `[0,1] and f(1/2)=1.` prove that `lim_(n->oo)f((sqrt(n))/(2sqrt(n+1)))=1`

A

0

B

`oo`

C

2

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Since, f(x) is continuous in [0, 1], therefore
`lim_(n to oo) f((sqrt(n))/(2sqrt(n)+1))=f(lim_(n to oo) (sqrt(n))/(2sqrt(n)+1))`
`=f((1)/(2))=2`
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 2 (MISCELLANEOUS PROBLEMS)|60 Videos

  • CONTINUITY

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|16 Videos

  • CIRCLE AND CONICS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise All Questions|74 Videos

  • DEFINITE INTEGRALS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|22 Videos

Similar Questions

Explore conceptually related problems

If f(x) is continuous in [0,1] and f((1)/(2))=1 prove that lim_(n rarr oo)f((sqrt(n))/(2sqrt(n+1)))=1

lim_(n rarr oo)(1+sqrt(n))/(1-sqrt(n))

lim_(n rarr oo)(sqrt(n+1)-sqrt(n))=0

lim_(n rarr oo)((sqrt(n+3)-sqrt(n+2))/(sqrt(n+2)-sqrt(n+1)))

The value of lim_(n rarr oo)[3sqrt((n+1)^(2))-3sqrt((n-1)^(2))] is

let f(x)=lim_(n rarr oo)(x^(2n)-1)/(x^(2n)+1)

If f is continuous and differentiable function and f(0)=1,f(1)=2, then prove that there exists at least one c in[0,1] for which f'(c)(f(c))^(n-1)>sqrt(2^(n-1)), where n in N.

f'(0) = lim_(n->oo) nf(1/n) and f(0)=0 Using this, find lim_(n->oo)((n+1)(2/pi)cos^(- 1)(1/n)-n)),|cos^(-1)1/n|