Two-Sided Limits : g(x,y)=|x|y (that's module sign) prove that g is not differentiable at (0,b) for any value non-zero value of b.
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G(x,y)=|x|y (that's module sign) prove that g is not differentiable at (0,b) for any value non-zero value of b.
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A two-sided limit proof is provided. The solution is detailed and well presented.
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Problem 56471:
For a function f(x) to be differentiable at a point x = a, the following limit must exist and be finite:
. A limit written like this is a "two-sided" limit.
When one writes a limit as above, it means a "two-sided" limit. This means that if x approaches a from the left or the right, the limits must be the same, or the two-sided limit doesn't exist, so the limit doesn't exist. This can be found in most calculus books.
We write this as:
exists if and only if = <> +/-infinity.
So now we can say that a function ...
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