Problem. Let , find g'(0) and prove that g'(x) is not continuous at x=0.
My work: , but g(0) is undefined, so how do you find the derivative?
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No, it is defined g(0)=0.
Well, then, I have
So g'(0) = 0?
Yes because now use squeeze theorem.
Now to prove g'(x) is not continuous at x = 0.
Pick a sequence that converges to 0.
I think I'm stuck...
To show that is not continous at zero (for example) a sequene say which is zero. And pick another sequence like which is 1. So it is not continous.
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