Home
Class 12
MATHS
Evaluate lim(ntooo) cos(pisqrt(n^(2)+n))...

Evaluate `lim_(ntooo) cos(pisqrt(n^(2)+n))` when n is an integer.

Text Solution

Verified by Experts

The correct Answer is:
0
`L=underset(ntooo)limcos(pisqrt(n^(2)+n))`
`=underset(ntooo)lim(-1)^(n)cos(npi-pisqrt(n^(2)+n))`
`=underset(ntooo)lim(-1)^(n)cos(pi(n-sqrt(n^(2)+n)))`
`=(-1)^(n)underset(ntooo)limcos((-npi)/(n+sqrt(n^(2)+n)))`
`=(-1)^(n)underset(ntooo)limcos((pi)/(1+sqrt(1+(1)/(n))))`
`=(-1)^(n)"cos"(pi)/(2)`
=0
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    CENGAGE|Exercise Exercise 2.4|5 Videos

  • LIMITS

    CENGAGE|Exercise Exercise 2.5|12 Videos

  • LIMITS

    CENGAGE|Exercise Exercise 2.2|7 Videos

  • JEE 2019

    CENGAGE|Exercise Chapter 10|9 Videos

  • LINEAR COMBINATION OF VECTORS, DEPENDENT AND INDEPENDENT VECTORS

    CENGAGE|Exercise DPP 1.2|10 Videos

Similar Questions

Explore conceptually related problems

Evaluate the limit: (lim_(n rarr oo)cos(pi sqrt(n^(2)+n)) when n is an integer

lim_(ntooo)(n-sqrt(n^(2)+n))

lim_(ntooo)cos (pisqrt(n^(2)+n)) (where n is an integer) is equal to

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

Evaluate lim_(ntooo)(pin)^(2//n)

lim_(n->oo)cos^2(pi(3sqrt(n^3+n^2+2n)-n)) where n is an integer,equals

Find the value of lim_(n rarr oo)cos[pi sqrt(n^(2)+n)],n in Z is equal to

Let f(x)=lim_(ntooo) (x)/(x^(2n)+1). Then

Evaluate lim_(ntooo) (n^(p)sin^(2)(n!))/(n+1),"wher "0ltplt1.