Test whether the function f(x) = begincases dfracx2 - 2xx - 2, & x ne | Basic Mathematics 2081

Basic Mathematics20815 marksNumerical: continuity testContinuity definition

Test whether the function $f(x) = \begin{cases} \dfrac{x^2 - 2x}{x - 2}, & x \ne 2 \\ 1, & x = 2 \end{cases}$ is continuous or discontinuous at $x = 2$ . Explain. [5]

Test whether the function $f(x) = \begin{cases} \dfrac{x^2 - 2x}{x - 2}, & x \ne 2 \ 1, & x = 2 \end{cases}$ is continuous or discontinuous at $x = 2$. Explain. [5]

$f(x) = \begin{cases} \dfrac{x^2 - 2x}{x - 2}, & x \ne 2 \\[2mm] 1, & x = 2 \end{cases}$ Point to test: $x = 2$ . A function $f$ is continuous at $x = a$ if: 1. $f(a)$ is defined, 2. $\lim{x \to a} f(x)$ exists, 3. $\lim{x \to a} f(x) = f(a)$ . $f(2) = 1 \quad \text{(defined)}$ For $x \ne 2$ :

$$f(x) = \begin{cases} \dfrac{x^2 - 2x}{x - 2}, & x \ne 2 \[2mm] 1, & x = 2 \end{cases}$$ Point to test: $x = 2$. A function $f$ is continuous at $x = a$ if: 1. $f(a)$ is defined, 2. $\lim{x \to a} f(x)$ exists, 3. $\lim{x \to a} f(x) = f(a)$. $$f(2) = 1 \quad \text{(defined)}$$ For $x \ne 2$:

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Test whether the function f(x) = begincases dfracx2 - 2xx - 2, & x ne 2 1, & x = 2 endcases is continuous or discontinuous at x = 2. Explain.