If limx→3f(x)=7, which of the following must be true? i. f is continuous at x = 3 ii. f is differentiable at x = 3

Without knowing anything else about , neither of these need be true.

Suppose

Then (I) isn't true because, while the limit exists as and is equal to 7, we have , so is not continuous there.

(II) also true because is not differentiable at ; that is,

but

which means the derivative does not exist at .

Neither of the statements is true.

Without knowing anything else about , neither of these needs to be true.

Suppose,

Then (I) isn't true because, while the limit exists as and is equal to , we have , so  is not continuous there.

(II) is also not true because   is not differentiable at ; that is,

but

which means the derivative does not exist at .

Learn more about limits and derivatives.

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