MediumMathematicsHigh School (11–12)Functions and Calculus › Continuity and DifferentiabilityNumericalBoard Exam

Let f(x) = (x² - 4)/(|x - 2|) for x ≠ 2…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Let $f(x) = \dfrac{x^2 - 4}{|x - 2|}$ for $x \ne 2$ . Find the left-hand limit and the right-hand limit of $f$ at $x = 2$ , and the size of the jump between them.

Need a reminder? The key ideaShow

A function $f$ is continuous at $a$ when $\displaystyle\lim_{x \to a^-} f(x) = \lim_{x \to a^+} f(x) = f(a)$ . If the one-sided limits differ, the break is a jump. If the limit exists but $f(a)$ differs, the break is removable.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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