Given the function f(x) = 1/(sqrt x)

Question

a. Does f(x) exist at x=0?
b. Does f'(x) exist at x=0?
c. Explain why integral (from 0->1) f(x)dx does exist.

THANK YOU.

Answer 1

a) no, one is not allowed to have zero in the denominator.
b. f(x)=1/sqrt(x)
f'= -1/(2 x^-3/2) yes it exists

c. if an endpoint does not exist, one cannot integrate it.

Answer 2

Thank you so much! but are you sure for part c.?

Answer 3

so idk the answer