use the hint ... change x to h and use the def. of a derivative
Will someone help me solve this? I tried to solve many times and keep getting 0 as the answer. Wolfram Alpha says the answer should be (secy)^2.
Without using any trigonometric identities, find
lim x->0 [tan(x + y) - tan y]/x
Hint: Relate the given limit to the definition of the derivative of an appropriate function of y.
I used tan(x + y) = (tan x + tan y)/(1 - tan x tan y). I still got 0 as the answer.
Initially I used the definition without changing the variables, i.e. So in a way, I had used the instruction which stated to use the definition of a derivative... I'm not sure that I used the hint in the way you referred.
At this point, I don't know what to do. I can't use L' Hopital's Rule yet because that is introduced later in the book.
... some middle steps
per Wolfram Alpha, not the solution's manual.
You said no trig identities, so the procedure you and Vlasev suggest, though valid, was not allowed.
You end up with the same result as Vlasev if you recognize
and the first factor is 1. But you only know that because of L'H˘pital's rule. You should see how to get from here to .
But the answer to the problem is given by skeeter - twice. And he actually uses the hint, which is always a good sign that you're on the right track. Do you see how skeeter's solution works?