Question

AP CALC derivative and limits, equation below!

lim as h→0 of ((1+h)^(10)−1)) / h

Answer 1

\[\lim_{h \rightarrow 0} \frac{ (1+h)^{10} -1 }{ h }\]

Answer 2

A tenth order binomial? Boy that would be a pain to expand out. We better use some limit tricks to get this one done.

Answer 3

I know that it is related to the definition of a derivative formula, so 1 is f(a). But where does the 10th play in?

Answer 4

Hmmmm, I think we're dealing with this.
\[\large f(x)=x^{10}\]
\[\large f'(1)=\lim_{h \rightarrow 0}\frac{ (1+h)^{10}-1^{10} }{ h }\]

Answer 5

So what would the limit be as h → 0? 10? 9? So losttt

Answer 6

Well, have you learned the power rule yet? That will give us an idea of what answer we SHOULD be looking for. But we still need to work through this limit I think :3 hmm

Answer 7

yeah i have, we're doing related rates now but we're having a big test & these problems will be on it too, so i'm reviewing.

Answer 8

would it be 10 because if f(x) = x^10 and you use power rule, then 10x^9 at x = 1 is 10?

Answer 9

Yes, good :)\[\large f'(x)=10x^9\]\[\large f'(1)=10(1)^9=10\]

Answer 10

Thank you! :D

Answer 11

So you just need the answer, you don't actually have to work through the limit? :)

Answer 12

Oh thank goodness c: lol