Hi.
I have 2 questions, first:
Say that there's f(x) = sqrt(x), I want to find the limit of the function at x = 0, so I have to check the right and left sided limits:
lim x->0+ sqrt(x) = sqrt(0) = 0
lim x->0- sqrt(x) = ?? (function isn't defined on a small interval to the left of zero)
thus, this limit doesn't exist right?
Second question:
It is said that if f(x) is continuous at x = a, and a is inside the interval f(x) >= 0, then g(x) = sqrt(f(x)) would be continuous at a
, what if a is at the edge of g(x) ? i mean it's a zero of the function g(x) (like 0 is the zero for sqrt(x)), wouldn't this function be discontinuous at x = a?
Thanks.
I have 2 questions, first:
Say that there's f(x) = sqrt(x), I want to find the limit of the function at x = 0, so I have to check the right and left sided limits:
lim x->0+ sqrt(x) = sqrt(0) = 0
lim x->0- sqrt(x) = ?? (function isn't defined on a small interval to the left of zero)
thus, this limit doesn't exist right?
Second question:
It is said that if f(x) is continuous at x = a, and a is inside the interval f(x) >= 0, then g(x) = sqrt(f(x)) would be continuous at a
, what if a is at the edge of g(x) ? i mean it's a zero of the function g(x) (like 0 is the zero for sqrt(x)), wouldn't this function be discontinuous at x = a?
Thanks.