Continuity and types of discontinuity practice problems
Find where a function is discontinuous and say whether each break is removable, a jump or infinite. 10 problems with worked solutions; in 10 of them every equation is proved by a computer algebra system.
Find every point where \( \displaystyle f(x) = \frac{x^{2} - 25}{x^{2} - 7 x + 10} \) is discontinuous, and classify each discontinuity as removable, a jump, or infinite.
Find every point where \( \displaystyle f(x) = \frac{2 x^{2} - 18 x + 40}{x^{2} - 2 x - 15} \) is discontinuous, and classify each discontinuity as removable, a jump, or infinite.
Find every point where \( \displaystyle f(x) = \frac{- x^{2} + 2 x + 15}{x^{2} - 7 x + 10} \) is discontinuous, and classify each discontinuity as removable, a jump, or infinite.
Find every point where \( \displaystyle f(x) = \frac{36 - 12 x}{x^{2} - 4 x + 3} \) is discontinuous, and classify each discontinuity as removable, a jump, or infinite.
Find every point where \( \displaystyle f(x) = \frac{- 2 x^{2} - 14 x - 24}{x^{2} + 3 x - 4} \) is discontinuous, and classify each discontinuity as removable, a jump, or infinite.
Find every point where \( \displaystyle f(x) = \frac{3 x^{2} - 3 x - 36}{x^{2} - 7 x + 12} \) is discontinuous, and classify each discontinuity as removable, a jump, or infinite.
Find every point where \( \displaystyle f(x) = \frac{2 x^{2} - 2}{x^{2} - x - 2} \) is discontinuous, and classify each discontinuity as removable, a jump, or infinite.
Find every point where \( \displaystyle f(x) = \frac{- 12 x - 24}{x^{2} + 3 x + 2} \) is discontinuous, and classify each discontinuity as removable, a jump, or infinite.
Find every point where \( \displaystyle f(x) = \frac{3 x^{2} + 9 x - 12}{x^{2} + x - 12} \) is discontinuous, and classify each discontinuity as removable, a jump, or infinite.
Find every point where \( \displaystyle f(x) = \frac{2 x^{2} + 4 x - 16}{x^{2} - x - 20} \) is discontinuous, and classify each discontinuity as removable, a jump, or infinite.