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

1. mortonsalt

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.

2. zepdrix

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:$\large\rm f(a+h)=(1+h)^{10},\qquad\qquad f(a)=1$

3. zepdrix

So ummm

4. zepdrix

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

5. zepdrix

$\large\rm f(\color{orangered}{a+h})=(\color{orangered}{1+h})^{10}$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.

6. zepdrix

Hopefully that helps :U Stay salty friend.

7. mortonsalt

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