How you slove this? #lim_(n->oo)cos(pisqrt(4n^2+n+1))# Calculus Differentiating Trigonometric Functions Limits Involving Trigonometric Functions 1 Answer Cesareo R. Mar 19, 2017 #1# Explanation: Assuming that #n in ZZ# #lim_(n->oo)cos(pisqrt(4n^2+n+1))=lim_(n->oo)cos(2 pi n sqrt(1+(n+1)/(4n^2))) = cos(2pi n)=1# Answer link Related questions How do you find the limit of inverse trig functions? How do you find limits involving trigonometric functions and infinity? What is the limit #lim_(x->0)sin(x)/x#? What is the limit #lim_(x->0)(cos(x)-1)/x#? What is the limit of #sin(2x)/x^2# as x approaches 0? Question #99ee1 What is the derivative of #2^sin(pi*x)#? What is the derivative of #sin^3x#? Question #eefeb Question #af14f See all questions in Limits Involving Trigonometric Functions Impact of this question 2929 views around the world You can reuse this answer Creative Commons License