Does f ' (0) Exists?

[nycmathguy]

Calculus
Section 2.7

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

 

[MathLover1]

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

 

[nycmathguy]

57.
given:

f'(a)=View attachment 3432

a=0

f'(0)=View attachment 3434


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?

 

[MathLover1]

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

 

[nycmathguy]

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

View attachment 3435

Much better.