Question #51d9b Calculus Differentiating Trigonometric Functions Limits Involving Trigonometric Functions 1 Answer Καδήρ Κ. Dec 26, 2017 #lim_{x->0^+}(sin2x)^(x^(-2))=0# Explanation: #lim_{x->0^+}(sin2x)^(x^(-2))=lim_{x->0^+}(sin2x)^(1/x^2)=# #lim_{x->0^+}e^(1/x^2*ln(sin2x))# Let's calculate this limit now : #lim_{x->0^+}ln(sin2x)*1/x^2=-oo# So now our limit becomes: #lim_{u->-oo}e^u=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 1691 views around the world You can reuse this answer Creative Commons License