Does f ' (0) Exists?

Calculus
Section 2.7



Can you do 57? I will then do 58 using your reply as a guide.

 

57.
given:



f'(a)=

a=0

f'(0)=


f'(0)=lim(h*sin(1/h))/h as h->0

f'(0)=lim(sin(1/h)) as h->0

f'(0)=lim(sin(1/0)) -> function oscillating no matter how far we go

so, limit f'(0) DNE

 

What do you mean by h tends to a box or square?

 

where do you see that "h tends to a box or square"?
ah, I see now on the image above
I was using wolfram alpha and didn't noticed it made a square instead of a

I said h->a

 

Much better.