Consider the sequence .
What is the value of
I have a homework assignement due tomorrow morning and I have some idea on how to do this problem but I am not very sure.
Define functions f and g on [-1,1] by
Prove that f is continous at 0 and that g is not continuous at 0. Explain why these functions are continuous at every other point in [-1,1].
So I was thinking for f(x) just using the definition of continuity:
Choose
Ok this proves that f is continuous at 0 right??
I am not entirely sure how to prove g(x) isn't continuous but also that these functions are continuous at every other points!
Any suggestion??
Well you don’t do that because it is not true of .
You proved that is not continuous at so it cannot be continuous for all .
You also proved that is continuous at .
Note that if then both functions are continuous.
The product of two continuous functions is continuous.