Home
Class 12
MATHS
If ("lim")(xveca)(a^x-x^a)/(x^x-a^a)=-1a...

If `("lim")_(xveca)(a^x-x^a)/(x^x-a^a)=-1a n da >0,` then find the value of`adot`

A

43529

B

2

C

`"sin"(2)/(5)`

D

`"sin"(1)/(5)`

Text Solution

Verified by Experts

The correct Answer is:
`a=1`
Since `underset(xtoa)lim(a^(x)-x^(a))/(x^(x)-a^(a))=-1" ,`
`underset(xtoa)lim(a^(x)loga-ax^(a-1))/(x^(x)(1+logx))=-1`
or `underset(xtoa)lim(a^(a)[loga-1])/(a^(a)[1+loga])=-1`
or` loga-1=-1-loga`
or` 2loga=0`
or` loga=0`
or` a=1`
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    CENGAGE PUBLICATION|Exercise Exercises (Single Correct Answer Type)|76 Videos

  • LIMITS

    CENGAGE PUBLICATION|Exercise Linked Comprehension Type|20 Videos

  • LIMITS

    CENGAGE PUBLICATION|Exercise EXERCISE 2.7|7 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

If lim_(x->a)(a^x-x^a)/(x^x-a^a)=-1 and a >0, then find the value of a.

If lim_(x->2)(x^n-2^n)/(x-2)=80 and n in N ,then find the value of n.

If ("lim")_(x tooo){(x^2-1)/(x+1)-(a x+b)}=2, then find the value of a and bdot

If lim_(xtooo) {(x^(2)+1)/(x+1)-(ax+b)}=0, then find the values of a and b.

If lim_(xto0) ((4x-1)^(1/3)+a+bx)/(x)=1/3 then find the values of a and b.

Let a >2 be a constant. If there are just 18 positive integers satisfying the inequality (x-a)(x-2a)(x-a^2)<0, then find the value of adot

If lim_(xtoa)[f(x)+g(x)]=2 and lim_(xtoa) [f(x)-g(x)]=1, then find the value of lim_(xtoa) f(x)g(x).

If f(x)=sqrt(x^2+a x+4) is defined for all x , then find the value of adot

If the lines x+(a-1)y+1=0 and 2x+a^2y-1=0 are perpendicular, then find the value of adot

Let f(x)=a/x+x^2dot If it has a maximum at x=-3, then find the value of adot