Show f(x) defined by f(x) = \(\begin{cases}\frac{x^2 - 25}{x - 5} &\;

1.	Show f(x) defined by f(x) = \(\begin{cases}\frac{x^2 - 25}{x - 5} &\; when\; x \neq 5\\10& \;when\; x = 5\end{cases}\) is continuous at x = 5
Answer» Also f(x) at x = 5 is 10; i.e, f(5) = 10 Here \(\lim\limits_{x \to 5}\) f(x) = f(5) = 10 ∴ the function f(x) is continuous at x = 5

Show f(x) defined by f(x) = \(\begin{cases}\frac{x^2 - 25}{x - 5} &\; when\; x \neq 5\\10& \;when\; x = 5\end{cases}\) is continuous at x = 5

Answer»

Also f(x) at x = 5 is 10; i.e, f(5) = 10

Here \(\lim\limits_{x \to 5}\) f(x) = f(5) = 10

∴ the function f(x) is continuous at x = 5

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