Home
Class 12
MATHS
If lim(xtoa)f(x)=1 and lim(xtoa)g(x)=oo ...

If `lim_(xtoa)f(x)=1` and `lim_(xtoa)g(x)=oo` then `lim_(xtoa){f(x)}^(g(x))=e^(lim_(xtoa)(f(x)-1)g(x))`
`lim_(xto0)((sinx)/x)^((sinx)/(x-sinx))` is equal to

A

(a) `1//e`

B

(b) `-1//e`

C

(c) `e`

D

(d) `-e`

Text Solution

Verified by Experts

The correct Answer is:
A
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • LIMITS

    ARIHANT MATHS|Exercise Exercise (Matching Type Questions)|3 Videos

  • LIMITS

    ARIHANT MATHS|Exercise MATCHING TYPE QUESTIONS|1 Videos

  • LIMITS

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|15 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|8 Videos

  • LOGARITHM AND THEIR PROPERTIES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|4 Videos

Similar Questions

Explore conceptually related problems

If lim_(xtoa)f(x)=1 and lim_(xtoa)g(x)=oo then lim_(xtoa){f(x)}^(g(x))=e^(lim_(xtoa)(f(x)-1)g(x)) lim_(xto0)((x-1+cosx)/x)^(1/x) is equal to

If lim_(xtoa)f(x)=1 and lim_(xtoa)g(x)=oo then lim_(xtoa){f(x)}^(g(x))=e^(lim_(xtoa)(f(x)-1)g(x)) lim_(xto0)((a^(x)+b^(x)+c^(x))/3)^(2/x) is equal to a. a^(2//3)+b^(2//3)+c^(2//3) b. abc c. (abc)^(2//3) d. 1

lim_(xto0)(e^(3x)-1)/(x) is :

lim_(xto0)((1-cos2x)(3+cosx))/(x tan 4x) is equal to

lim_(xto0)(sin(picos^(2)(tan(sinx))))/(x^(2)) is equal to

lim_(xto0)(1-cos(x^(2)))/(x^(3)(4^(x)-1)) is equal to:

Evaluate lim_(xto0^(+))(sinx)^(x)

lim_(xto0) (e^(tanx)-e^x)/(tanx-x)=

Slove lim_(xto0)((1+x)^(1//x)-e)/x

Find lim_(xto0+)(cot^(-1)(1/x))/x

Home
Profile