Problem :
Is the following function continuous: f (x) = 3x2 + 2? If not, what type
of discontinuity exists?
Yes, it is continuous -- it is a polynomial.
Problem :
Is the following function continuous: f (x) =
? If not, what type
of discontinuity exists?
No, it is discontinuous. There exists an infinite discontinuity at
x = 0.
Problem :
Is the following function continuous: f (x) = tan(x)? If not, what type of
discontinuity exists?
No, it is discontinuous. An infinite discontinuity exists at the points
x =
+ nΠ, where
n is any integer.
Problem :
Is the following function continuous: f (x) =
? If not, what
type of discontinuity exists?
No, it is discontinuous. At
x = 0, a point discontinuity exists.
Problem :
Is the following function continuous: f (x) =
x)? If not, what type of
discontinuity exists?
Yes, it is continuous (for all
x > 0, of course--this is the domain of the
function).