Finding the meaning of a limit using a graph

[ttpp1124]

Homework Statement

The graph is a separate image (it didn't print with the worksheet for some reason). I filled in the blanks, but I wasn't sure how to approach part b)

Relevant Equations

n/a

 

[Eclair_de_XII]

I filled in the blanks, but I wasn't sure how to approach part b)

I should think that you can find the meaning of that expression in your calculus book. As for the value, you will probably need to review limits in order to evaluate it properly.

 

[FactChecker]

Imagine you have small, tiny, values for h, (both positive and negative?). Then look at the graph and see what that formula would give. The formula is in the form of "the rise over the run" at a particular value of x. Do you know what value of x it is located at? Do you know what that leads to?

 

[Mustard]

I suggest you look up "derivatives and sharp turns" for the meaning and value at x= -2.

 

[Mark44]

You posted the same question in a new thread. This was your answer in that thread.

My answer for 12b:
If the limit exists, it’s the derivative of 𝑓 at 𝑥=−2. But, the limit doesn’t exist. To see this, calculate the one-sided limits as h approaches zero from the right, and from the left. They both exist, but they are not the same, so the limit does not exist, meaning 𝑓 is not differentiable at 𝑥=−2

Correct, but please don't start a new thread for the same question. I have deleted the new thread.

 

[haruspex]

I worry that perhaps they meant to write h→0⁺. Or maybe that's the trap you avoided.