Home
Class 12
MATHS
Let p=lim(xto0^(+))(1+tan^(2)sqrt(x))^((...

Let `p=lim_(xto0^(+))(1+tan^(2)sqrt(x))^((1)/(2x))`. Then `log_(e)p` is equal to

Text Solution

Verified by Experts

The correct Answer is:
B
`p=underset(xto0^(+))lim(1+tan^(2)sqrt(x))^((1)/(2x))(1^(oo)" form")`
`=e^(underset(xto0)lim(1+tan^(2)sqrt(x)-1)(1)/(2x))=e^(underset(xto0+)lim((tansqrt(x))^(2))/(2(sqrt(x))^(2)))=e^((1)/(2))`
`:." "log_(e)p=log_(e)^((1)/(2))=(1)/(2)`
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    CENGAGE PUBLICATION|Exercise Archives JEE ADVANCED|2 Videos

  • LIMITS

    CENGAGE PUBLICATION|Exercise Single Correct Answer Type|59 Videos

  • LIMITS

    CENGAGE PUBLICATION|Exercise Numerical Value Type|26 Videos

  • JEE 2019

    CENGAGE PUBLICATION|Exercise Chapter 10|8 Videos

  • LINEAR COMBINATION OF VECTORS, DEPENDENT AND INDEPENDENT VECTORS

    CENGAGE PUBLICATION|Exercise DPP 1.2|10 Videos

Similar Questions

Explore conceptually related problems

Let p=underset(x to 0^(+))lim(1+tan^(2)sqrt(x))^((1)/(2x)) then log p is equal to

lim _(xto0) (a ^(x) -b^(x))/(e ^(x)-1)

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

Evaluate lim_(xto1) ((2x-3)(sqrt(x)-1))/(2x^(2)+x-3).

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

lim_(xto0) (sqrt(1-cos 2x))/(sqrt2x) is equal to-

Evaluate: lim_(xto0)[tan(x+(pi)/(4))]^(1//x)

Evaluate lim_(xto0)(sin^(-1)x-tan^(-1)x)/(x^(3)).

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

The value of lim_(x to 0) (27^(x)-9^(x)-3^(x)+1)/(log_(e)(1+(x^(2))/(2))) is equal to -