lim(xrarr(pi))(sinx)/(x-pi) is equal to...

`lim_(xrarr(pi))(sinx)/(x-pi)` is equal to

A

1

B

2

C

`-1`

D

`-2`

Text Solution

Verified by Experts

The correct Answer is:

C

Given, `lim_(xto(pi))(sinx)/(x-pi)` `[therefore sintheta=sin(pi-theta)]`
`=-lim_(xto(pi))(sin(pi-x))/(pi-x)=-1` `[therefore lim_(xto0)(sinx)/(x)=1 " and " xto0 rArr xto(pi)]`

Doubtnut Promotions Banner Desktop Dark

Doubtnut Promotions Banner Mobile Dark

|

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

Similar Questions

Explore conceptually related problems

lim_(xrarr0) (sinx)/(x)= ?

(lim_(1))_(x rarr1)(sin pi x)/(x-1) is equal to -pi b*pi c*-(1)/(pi) d.(1)/(pi)

Knowledge Check

lim_(xrarr0^-)(sinx)/(sqrt(x)) is equal to

A

0

B

1

C

`-(1)/(2)`

D

none of these

lim_(xrarr0)(|sinx|)/(x) is equal to

A

1

B

`-1`

C

Does not exist

D

None of these

lim_(xrarr0)(tan2x-x)/(3x-sinx) is equal to

A

2

B

`1/2`

C

`-1/2`

D

`1/4`

Similar Questions

Explore conceptually related problems

lim_(xrarr0)(cos(sinx)-1)/x^2 is equal to

lim_(x to pi/2)(1-sinx)/(cosx) is equal to :

lim_(xrarr0)(e^(sinx)-1)/x is equal to

lim_(xrarr0)(tanx-sinx)/x^3 is equal to

If f(x)=int_1^xsin^2(t/2)dt , then the value of lim_(xrarr0)(f'(pi+x)-f(x))/x is equal to

NCERT EXEMPLAR-LIMITS AND DERIVATIVES -OBJECTIVE TYPE QUESTIONS

lim(xrarr(pi))(sinx)/(x-pi) is equal to
01:41
|
lim(xrarr0)(x^(2)cosx)/(1-cosx) is equal to
03:53
|
lim(xrarr0)((1+x)^(n)-1)/(x) is equal to
02:04
|
lim(xrarr1)(x^(m)-1)/(x^(n)-1) is equal to
02:23
|
lim(thetato0)(1-cos4theta)/(1-cos6theta) is equal to
03:47
|
lim(xrarr0)("cosec"x-cotx)/(x) is equal to
03:21
|
lim(xrarr0)(sinx)/(sqrt(x+1)-sqrt(1-x)) is equal to
02:54
|
lim(xrarr(pi//4))(sec^2x-2)/(tanx-1) is
02:32
|
lim(x->1)[(2x-3)(sqrtx-1)]/[2x^2+x-3]
03:42
|
If f(x) = { sin[x] /[x],[x] != 0 ; 0, [x] = 0} , Where[.] denotes the ...
02:12
|
lim(xrarr0)(|sinx|)/(x) is equal to
02:36
|
If f(x) ={x^2-1, 0 lt x lt 2 , 2x+3 , 2 le x lt 3then the quadratic eq...
02:42
|
lim(xrarr0)(tan2x-x)/(3x-sinx) is equal to
02:12
|
if f(x) =x-[x], in R, then f^(')(1/2) is equal to
03:19
|
if y=sqrt(x) + 1/sqrt(x), then (dy)/(dx) at x=1 is equal to
02:52
|
If f(x) =(x-4)/(2sqrt(x)), then f^(')(1) is equal to
03:13
|
if y=(1+1/x^(2))/(1-1/(x)^(2)),then (dy)/(dx) is equal to
03:10
|
if y=(sinx+cosx)/(sinx-cosx), then (dy)/(dx) at x=0 is equal to
03:45
|
if y=(sin(x+9))/(cosx), then (dy)/(dx) at x=0 is equal to
03:39
|
If f(x)=1+x+(x^2)/2++(x^(100))/(100), then f^(prime)(1) is equal to
03:27
|