Home
Class 12
MATHS
Evaluate lim(xto0) (sin[cosx])/(1+[cosx]...

Evaluate `lim_(xto0) (sin[cosx])/(1+[cosx])` (`[.]` denotes the greatest integer function).

Text Solution

Verified by Experts

The correct Answer is:
0
When `xto0^(+)" or "0^(-),cosxto1^(-)`
or `" "[cosx]=0" for "xto0`
`:." "underset(xto0)lim(sin[cosx])/(1+[cosx])=(sin0)/(1+0)=0`
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    CENGAGE|Exercise Exercise 2.2|7 Videos

  • LIMITS

    CENGAGE|Exercise Exercise 2.3|15 Videos

  • LIMITS

    CENGAGE|Exercise Question Bank|30 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

Evaluate: (lim)_(x rarr0)(sin[cos x])/(1+[cos x])([.] denotes the greatest integer function).

The value of lim_(xto0)(sin[x])/([x]) (where [.] denotes the greatest integer function) is

("lim")_(x→0^+)("sin"[cosx])/(1-[cosx]) ([.] denotes the greatest integer function) is equal to equal to 1 (b) equal to 0 does not exist (d) none of these

Evaluate: lim_(xto(5pi)/(4)) [sinx+cosx] , [.] denotes the greatest integer function.

Evaluate lim_(xto0) (cosx)^(cotx).

Evaluate lim_(xto2)(3+sinx)/(cosx)

lim_(x->0)(sin[sec^2x])/(1+[cosx]), where [*] denotes greatest integral function, is

Evalute [lim_(xto0) (sin^(-1)x)/(x)]=1 , where [*] represets the greatest interger function.

Prove that [lim_(xto0) (sinx)/(x)]=0, where [.] represents the greatest integer function.