lim(xrarr0)(x^(2)cosx)/(1-cosx) is equal...

`lim_(xrarr0)(x^(2)cosx)/(1-cosx)` is equal to

A

2

B

`3/2`

C

`-3/2`

D

1

Text Solution

Verified by Experts

The correct Answer is:

A

Given, `lim_(xto0)(x^(2)cosx)/(1-cosx)` `[therefore 1-cosx=2sin^(2)((x)/2)]`
`=2lim_(xto0)(x/2)^(2)/(sin^(2)(x/2))lim_(xto0)cosx=2.1=2`

Promotional Banner

Promotional Banner

Topper's Solved these Questions

LIMITS AND DERIVATIVES
NCERT EXEMPLAR|Exercise FILLERS|4 Videos
LIMITS AND DERIVATIVES
NCERT EXEMPLAR|Exercise LONG ANSWER TYPE QUESTIONS|11 Videos
INTRODUCTION TO THREE DIMENSIONAL GEOMETRY
NCERT EXEMPLAR|Exercise Fillers|16 Videos
LINEAR INEQUALITIES
NCERT EXEMPLAR|Exercise Objective Type Questions|14 Videos

NCERT EXEMPLAR-LIMITS AND DERIVATIVES -OBJECTIVE TYPE QUESTIONS

lim(xrarr(pi))(sinx)/(x-pi) is equal to
Text Solution
|
lim(xrarr0)(x^(2)cosx)/(1-cosx) is equal to
Text Solution
|
lim(xrarr0)((1+x)^(n)-1)/(x) is equal to
Text Solution
|
lim(xrarr1)(x^(m)-1)/(x^(n)-1) is equal to
Text Solution
|
lim(thetato0)(1-cos4theta)/(1-cos6theta) is equal to
Text Solution
|
lim(xrarr0)("cosec"x-cotx)/(x) is equal to
Text Solution
|
lim(xrarr0)(sinx)/(sqrt(x+1)-sqrt(1-x)) is equal to
Text Solution
|
lim(xrarr(pi//4))(sec^2x-2)/(tanx-1) is
Text Solution
|
lim(x->1)[(2x-3)(sqrtx-1)]/[2x^2+x-3]
Text Solution
|
If f(x) = { sin[x] /[x],[x] != 0 ; 0, [x] = 0} , Where[.] denotes the ...
Text Solution
|
lim(xrarr0)(|sinx|)/(x) is equal to
Text Solution
|
If f(x) ={x^2-1, 0 lt x lt 2 , 2x+3 , 2 le x lt 3then the quadratic eq...
Text Solution
|
lim(xrarr0)(tan2x-x)/(3x-sinx) is equal to
Text Solution
|
if f(x) =x-[x], in R, then f^(')(1/2) is equal to
Text Solution
|
if y=sqrt(x) + 1/sqrt(x), then (dy)/(dx) at x=1 is equal to
Text Solution
|
If f(x) =(x-4)/(2sqrt(x)), then f^(')(1) is equal to
Text Solution
|
if y=(1+1/x^(2))/(1-1/(x)^(2)),then (dy)/(dx) is equal to
Text Solution
|
if y=(sinx+cosx)/(sinx-cosx), then (dy)/(dx) at x=0 is equal to
Text Solution
|
if y=(sin(x+9))/(cosx), then (dy)/(dx) at x=0 is equal to
Text Solution
|
If f(x)=1+x+(x^2)/2++(x^(100))/(100), then f^(prime)(1) is equal to
Text Solution
|