Question

Problem: Find the limit of (tan^2x)/x as x approaches 0.

I'm having a hard time with this problem (I'm a bit rusty on trig). The hint that my teacher gave was: tanx=sinx/cosx.

Answer 1

so
\[\lim_{x\to 0}\frac{\sin(x)}{x\cos(x)}\]
\[=\lim_{x\to 0}\frac{\sin(x)}{x}\lim_{x\to 0}\frac{1}{\cos(x)}\] and now it should be easy

Answer 2

@satellite73, the tangent's being squared, but you get the same result.

Alternatively, you can say that \(\tan x\approx x\) for \(x\) near 0, so you have
\[\lim_{x\to0}\frac{\tan^2x}{x}=\lim_{x\to0}\frac{x^2}{x}=\lim_{x\to0}x\]

Answer 3

Thank you for the help. I was able to solve it.