Question

Limits...can someone just explain how i go about these kinds of problems?


**Posting pic

Answer 1

The limit definition of the derivative is:
\[\large \lim_{h\to0}\frac{f(x+h)-\color{red}{f(x)}}{h}\]


\[\large \lim_{h\to0}\frac{(1+h)^6-\color{red}{1}}{h}\]

Something to keep in mind, that red 1 is actually 1^6. Let's write it that way.

\[\large \lim_{h\to0}\frac{(1+h)^6-\color{red}{1^6}}{h}\]

Answer 2

It can be a little tricky to recognize what's going on with these sometimes.
I wrote it as 1^6 so it matches the form of the definition.

We see that our function \(\large f\) is going to be,

\(\large f(x)=x^6\)

And what do you suppose our c value is? :o

Answer 3

If our function is \(\large f(x)=x^6\)
Then the derivative would be,\[\large \lim_{h\to0}\frac{(x+h)^6-x^6}{h}\]But that's not quite what we have, our function is being evaluated at a particular point.

Answer 4

i believe c would equal 1

Answer 5

Yay good job c:

Answer 6

thank you so much(: