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Continuity and Limits

Problems

Continuity

How to Cite This SparkNote

Problem : Is the following function continuous: f (x) = 3x 2 + 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 = + , 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).

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