The following problems involve the CONTINUITY OF A FUNCTION OF ONE VARIABLE. Function y = f(x) is continuous at point x=a if the following three conditions are satisfied :

i.) f(a) is defined ,

ii.) $ \displaystyle{ \lim_{ x \to a } \ f(x) } $ exists (i.e., is finite) ,


iii.) $ \displaystyle{ \lim_{ x \to a } \ f(x) } = f(a) $ .

Function f is said to be continuous on an interval I if f is continuous at each point x in I. Here is a list of some well-known facts related to continuity :

Most problems that follow are average. A few are somewhat challenging. All limits are determined WITHOUT the use of L'Hopital's Rule. If you are going to try these problems before looking at the solutions, you can avoid common mistakes by using the above step-by-step definition of continuity at a point and the well-known facts, and by giving careful consideration to the indeterminate form $ \displaystyle{ ^{^{^{^{''}}}}{0 \over 0}^{''} }$ during the computation of limits. Knowledge of one-sided limits will be required. For a review of limits and indeterminate forms click here.

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Duane Kouba