Home
Class 12
MATHS
Evaluate lim(ntooo) (1)/(n^(2(log(e)n-lo...

Evaluate `lim_(ntooo) (1)/(n^(2(log_(e)n-log_(e)(n+1)))+n)`.

Text Solution

Verified by Experts

`underset(ntooo)lim(1)/(n^(2(log_(e)n-log_(e)(n-1)))+n)`
`=underset(ntooo)lim(1)/(n^(2)("log"_(e)(n)/(n+1))+n)`
`=underset(ntooo)lim(1)/(n^(2)("log"_(e)(1)/(1+(1)/(n)))+n)`
`=underset(xto0)lim(1)/((1)/(x^(2))("log"_(e)(1)/(1+x))+(1)/(x))`
`=underset(xto0)lim(1)/(-(log_(e)(1+x))/(x^(2))+(1)/(x))`
`=underset(xto0)lim(x^(2))/(x-log_(e)(1+x))`
`=underset(xto0)lim(x^(2))/(x-(x-(x^(2))/(2)))=2`
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    CENGAGE PUBLICATION|Exercise EXERCISE 2.1|10 Videos

  • LIMITS

    CENGAGE PUBLICATION|Exercise EXERCISE 2.2|7 Videos

  • LIMITS

    CENGAGE PUBLICATION|Exercise Comprehension Type|4 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

Evaluate lim_(xto1) (x^(2)+xlog_(e)x-log_(e)x-1)/((x^(2))-1)

Evaluate lim_(xto0) (x)^((1)/(log_(e)sinx)).

Evaluate lim_(hto0) (log_(e)(1+2h)-2log_(e)(1+h))/(h^(2)).

Evaluate lim_(xtooo) (log_(e)x)/(x)

Evaluate lim_(ntooo) (1)/(1+n^(2))+(2)/(2+n^(2))+...+(n)/(n+n^(2)).

Evaluate lim_(ntooo) n^(-n^(2))[(n+2^(0))(n+2^(-1))(n+2^(-2))...(n+2^(-n+1))]^(n) .

Evaluate lim_(ntooo) nsin(2pisqrt(1+n^(2))),(n inN).

Evaluate: lim_(n->oo)(4^n+5^n)^(1/n)

The value of lim_(ntooo) [(1)/(n)+(e^(1//n))/(n)+(e^(2//n))/(n)+...+(e^((n-1)//n))/(n)] is

The value of lim_(ntooo) [root(3)((n+1)^(2))-root(3)((n-1)^(2))] is __________.