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 2280 views around the world You can reuse this answer Creative Commons License