Show that the function f(x) = \(\begin{cases}(1 + 3x)^\frac{1}{2} ; x

1.	Show that the function f(x) = \(\begin{cases}(1 + 3x)^\frac{1}{2} ; x \neq0\\e^3 ; x = 0\end{cases}\) is continuous at x = 0.
Answer» \(\lim\limits_{x \to 0} f(x) = \lim\limits_{x \to 0} (1 + 3x)^\frac{1}{3} = e^3 = f(0)\) ∴ f(x) is continuous at x = 0

Show that the function f(x) = \(\begin{cases}(1 + 3x)^\frac{1}{2} ; x \neq0\\e^3 ; x = 0\end{cases}\) is continuous at x = 0.

Answer»

\(\lim\limits_{x \to 0} f(x) = \lim\limits_{x \to 0} (1 + 3x)^\frac{1}{3} = e^3 = f(0)\)

∴ f(x) is continuous at x = 0

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Show that the function f(x) = \(\begin{cases}(1 + 3x)^\frac{1}{2} ; x \neq0\\e^3 ; x = 0\end{cases}\) is continuous at x = 0.

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