Expert: Steve Holleran - 10/24/2007

Question
I'm not sure how to approach this question at all.

lim as h->0 of tan2(x+h)-tan(2x)/h

Can the h be factored out? Otherwise it would be undefined right? Thanks!

Answer
Hi Kaylee,

I'm not sure what stage of Calculus you are at, but what you want to do here is recognize this limit as the defintion of the derivative of tan(2x).

The definition of the derivative is

lim(h-->0) [f(x+h) -f(x)]/ h

so if you look on the top, "tan 2x" is where the "f(x)" is , and the rest of the limit fits the defintion,

so, the derivative of f(x) = tan(2x) would be

   2 * sec^2 (2x) and this would be the answer.


In any case, algebraically you absolutely cannot "factor out" the h!  This would be a nightmare to do algebraically.
Steve