Question

finding the limit (Problem is attached)

Answer 1

The limit in question represents the derivative of the function \[f(x)=\cos{(x^7)}\]Applying the Chain Rule, we see that \[f'(x)=-7x^6\sin{(x^7)}\] This is the value of the limit.

Answer 2

Do you plug 0 in for that to find the limit?

Answer 3

Is the limit 0 or -7x^6 sin(x^7)?

Answer 4

You do not need to plug in zero. The answer is the function \[-7x^6\sin{(x^7)}\]. Remember the definition of the derivative of a function
\[f'(x)=\lim_{h\to 0}\frac{f(x + h) - f(x)}{h}\]. If you look at your limit, you can see that it is of this form for \[f(x)=\cos{(x^7)}\]