Home
Class 12
MATHS
Evaluate lim(xto0) (sqrt(2)-sqrt(1+cosx)...

Evaluate `lim_(xto0) (sqrt(2)-sqrt(1+cosx))/(sin^(2)x).`

Text Solution

Verified by Experts

The correct Answer is:
`1//4sqrt(2)`
We have `underset(xto0)lim(sqrt(2)-sqrt(1+cosx))/(sin^(2)x)`
`underset(xto0)lim(2-(1+cosx))/(sin^(2)x)xx(1)/(sqrt(2)+sqrt(1+cosx))`
`=underset(xto0)lim(1-cosx)/((1+cosx)(1-cosx))xxunderset(xto0)lim(1)/(sqrt(2)+sqrt(1+cosx))`
`=underset(xto0)lim(1)/((1+cosx))xx(1)/(2sqrt(2))`
`=(1)/(4sqrt(2))`
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    CENGAGE|Exercise Exercise 2.4|5 Videos

  • LIMITS

    CENGAGE|Exercise Exercise 2.5|12 Videos

  • LIMITS

    CENGAGE|Exercise Exercise 2.2|7 Videos

  • JEE 2019

    CENGAGE|Exercise Chapter 10|9 Videos

  • LINEAR COMBINATION OF VECTORS, DEPENDENT AND INDEPENDENT VECTORS

    CENGAGE|Exercise DPP 1.2|10 Videos

Similar Questions

Explore conceptually related problems

lim_(xto0)(sqrt2-sqrt(1+cosx))/(sin^(2)x)

Evaluate lim_(xto0)(sqrt(1+x)+sqrt(1-x))/(1+x)

Evaluate the limits lim_(xto 0) (sqrt2-sqrt(1+cosx))/(sin^2x)

Evaluate lim_(xto0) (2^(x)-1)/(sqrt(1+x)-1).

Evaluate lim_(xto1)(sqrt(x^(2)-1)+sqrt(x-1))/(sqrt(x^(2)-1)) if xgt1 .

Evaluate lim_(xto0)(4^(x)-1)/(sqrt(1+x)-1)

Evaluate: lim_(xto0)(3^(x)-1)/(sqrt(1+x)-1)

Evaluate lim_(xto0) (1-cos(1-cosx))/(x^(4)).

Evaluate lim_(xto0)(cosx)/(pi-x)