Evaluate limit as x approaches 0 of:

Question

csc^2(7x)tan(2x^2)

Answer 1

well, we all know that as x->0,

x/sinx -> 1
tanx/x -> 1

csc^2(7x) = (7x)^2 / (7x^2)sin^2(7x)
tan(2x^2) = (2x^2)tan(2x^2) / (2x^2)

multiply those together, and recognizing the limits of 1, you wind up with

(2x^2)/(7x)^2 = 2/49

Answer 2

Thanks