How do you find the limit of # (sin^2(x^2))/(x^4)# as x approaches 0? Calculus Limits Determining Limits Algebraically 1 Answer SagarStudy Mar 3, 2016 #1# Explanation: Let #f(x)=(sin^2(x^2))/x^4# #implies f'(x)=lim_(x to 0) (sin^2(x^2))/x^4# #implies f'(x)=lim_(x to 0) (sin(x^2)*sin(x^2))/x^4=lim_(x to 0) {sin(x^2)/x^2*sin(x^2)/x^2}=lim_(x to 0)sin(x^2)/x^2lim_(x to 0)sin(x^2)/x^2*=1*1=1# Answer link Related questions How do you find the limit #lim_(x->5)(x^2-6x+5)/(x^2-25)# ? How do you find the limit #lim_(x->3^+)|3-x|/(x^2-2x-3)# ? How do you find the limit #lim_(x->4)(x^3-64)/(x^2-8x+16)# ? How do you find the limit #lim_(x->2)(x^2+x-6)/(x-2)# ? How do you find the limit #lim_(x->-4)(x^2+5x+4)/(x^2+3x-4)# ? How do you find the limit #lim_(t->-3)(t^2-9)/(2t^2+7t+3)# ? How do you find the limit #lim_(h->0)((4+h)^2-16)/h# ? How do you find the limit #lim_(h->0)((2+h)^3-8)/h# ? How do you find the limit #lim_(x->9)(9-x)/(3-sqrt(x))# ? How do you find the limit #lim_(h->0)(sqrt(1+h)-1)/h# ? See all questions in Determining Limits Algebraically Impact of this question 2637 views around the world You can reuse this answer Creative Commons License