What is #lim_(xrarrpi/2) e^(-tan^2x# ? Calculus Differentiating Trigonometric Functions Limits Involving Trigonometric Functions 1 Answer Gerardina C. Feb 4, 2018 #lim_(x->pi/2)e^(-tan^2x)=0# Explanation: Since #lim_(x->pi/2)tanx=+oo# we get #lim_(x->pi/2)tan^2x=+oo# #lim_(x->pi/2)-tan^2x=-oo# #lim_(x->pi/2)e^(-tan^2x)=e^-oo=1/e^(+oo)=1/oo=0# 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 2106 views around the world You can reuse this answer Creative Commons License