Home
Class 12
MATHS
Evaluate lim(xto1) ("cos"(pi)/(2)x)/(1-s...

Evaluate `lim_(xto1) ("cos"(pi)/(2)x)/(1-sqrt(x))`

A

-1

B

1

C

0

D

does not exist

Text Solution

Verified by Experts

The correct Answer is:
`pi`
`underset(xto1)lim("cos"(pi)/(2)x)/(1-sqrt(x))" "`(form 0/0)
`=underset(xto1)lim((-pi)/(2)"sin"((pi)/(2)x))/(-(1)/(2sqrt(x)))`
`=((pi)/(2)xx1)/((1)/(2sqrt(1)))=(pi)/(2)xx2=pi`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • LIMITS

    CENGAGE ENGLISH|Exercise Exercises (Single Correct Answer Type)|76 Videos

  • LIMITS

    CENGAGE ENGLISH|Exercise Multiple Correct Answers Type|24 Videos

  • LIMITS

    CENGAGE ENGLISH|Exercise EXERCISE 2.7|7 Videos

  • JEE 2019

    CENGAGE ENGLISH|Exercise Chapter 10|9 Videos

  • LINEAR COMBINATION OF VECTORS, DEPENDENT AND INDEPENDENT VECTORS

    CENGAGE ENGLISH|Exercise DPP 1.2|10 Videos

Similar Questions

Explore conceptually related problems

Evaluate lim_(xto0) (1-cos2x)/x^(2)

Evaluate lim_(xto1) (1-x)"tan"(pix)/(2).

Evaluate lim_(xto0)x^(3)"cos"2/x .

Evaluate lim_(xto1) (x^(4)-sqrt(x))/(sqrt(x)-1) .

Evaluate lim_(xto1) ((2)/(1-x^(2))-(1)/(1-x)).

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

Evaluate lim_(xto0){tan((pi)/4+x)}^(1/x)

Evaluate lim_(xto1) "sec" (pi)/(2^(x)).log_(e)x .

Evaluate lim_(xto-1^(+))(sqrt(pi)-sqrt(cos^(-1)x))/(sqrt(1+x)).

Evaluate lim_(xto1) ((2x-3)(sqrt(x)-1))/(2x^(2)+x-3).

Home
Profile