Home
Class 12
MATHS
Evaluate lim(xto pi) (sin^(-1)(1+cosx).s...

Evaluate `lim_(xto pi) (sin^(-1)(1+cosx).sec((x)/(2)))/((x-pi)).`

Text Solution

Verified by Experts

`underset(xto pi)lim(sin^(-1)(1+cosx).sec((x)/(2)))/((x-pi))" "`(0/0 from)
`=underset(xto pi)lim(sin^(-1)(1+cosx))/((1+cosx)).(1+cosx)/(cos((x)/(2))).(1)/((x-pi))`
`=1xxunderset(xto pi)lim(2cos^(2)((x)/(2)))/(cos((x)/(2))).(1)/((x-pi))`
`=underset(xto pi)lim(2cos((x)/(2)))/((x-pi))`
`=underset(xto pi)lim(sin((pi)/(2)-(x)/(2)))/(x/2-pi/2)=-1`
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    CENGAGE ENGLISH|Exercise Solved Examples|15 Videos

  • LIMITS

    CENGAGE ENGLISH|Exercise EXERCISE 2.1|10 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

Evalaute lim_(xto0) (x2^(x)-x)/(1-cosx)

Evaluate lim_(xto(pi)/(4)) (1-sin2x)/(1+cos4x).

Evaluate, lim_(xto(pi//4)) (sinx-cosx)/(x-pi/4)

Evaluate lim_(xto (pi^(-))/(2)) (cosx)^(cosx).

Evaluate: lim_(xto0)(log(e^(x)-x))/(1-cosx)

Evaluate lim_(xto(pi)/(2)) (1+cos2x)/((pi-2x)^(2)).

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

Evaluate lim_(xto pi//2) tanxlogsinx

Evaluate lim_(xto2) sin(e^(x-2)-1)/(log(x-1))

Evaluate: ("lim")_(x->pi/2)(cosx)^(cosx)