Question

Hello! I was wondering if someone can take a look at this question? (I'll post it below.)

Answer 1

The following limit represents the derivative of some function f at some number a.

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

State f and a.

Answer 2

We have the limit definition of a derivative:\[\large\rm f'(a)=\lim\limits_{h\to0}\frac{f(a+h)-f(a)}{h}\]
If you match up the pieces with the formula:\[\large\rm f(a+h)=(1+h)^{10},\qquad\qquad f(a)=1\]

Answer 3

So ummm

Answer 4

\[\large\rm f(\color{orangered}{a+h})=(\color{orangered}{1+h})^{10},\qquad\qquad f(a)=1\]If you look at this orange part here, you might be able to figure out what your a value is.

Answer 5

\[\large\rm f(\color{orangered}{a+h})=(\color{orangered}{1+h})^{10}\]And then if you choose to evaluate this at x, instead of a+h,\[\large\rm f(\color{orangered}{x})=(\color{orangered}{x})^{10}\]you should be able to see what your function is.
See if this matches up with f(a)=1 though.

Answer 6

Hopefully that helps :U
Stay salty friend.

Answer 7

Sorry this took forever for me to check again. Thank you so much for your help @zepdrix