Question

When x->0 lim TAN(x2)/ x =

Answer 1

tan = sin/cos

sin/cos sin
------ = -----
x x cos

sin(x^2) = (x^2) - (x^2)^3/3! + (x^2)^5/5! - ...
x cos(x^2) = x - x(x^2)^2/2! + x(x^2)^4/4! + x(x^2)^6/6! - ...

i spose we can try a Lhopital?

Answer 2

tan(x^2) to sec^2(x^2) 2x
x to 1

looks to go zero to me

Answer 3

we could have gone with the series of tan(x^2)/2 and seen that its a poly of x terms