Proving: Explain why s'(a) = lim [s(x)-s(a)]/[x-a] as x -&gt

[samantha0417]

Let S be a function that is differentiable at x=a

Part 1: Explain why s'(a) = lim as x approaches a [s(x)-s(a)]/[x-a]

Part 2: Explain, using the Part 1, s(x)-s(a)=([s(x)-s(a)]/[x-a])*(x-a)

Part 3: Why does the result in Part 2 display that f is continuous at x=a?

 

[pka]

The answer to all parts of your question is simple.
APPLY THE DEFINITION.

 

[samantha0417]

the definition of limits or derivatives?

 

[stapel]

How does your book define "derivative"?

Thank you.

Eliz.