Let $f(x) = \left\{ \begin{array}{r} 5^{1/x},\ \ x

Question

Let $f(x) = \left\{ \begin{array}{r} 5^{1/x},\ \ x < 0 \ \lambda\lbrack xbrack,\ \ \ \ x \geq 0 \end{array} ight.\$ and $\lambda \in R$, then at $x = 0$

Dr. Abubacker · Accepted Answer

(c)
$\lim_{x ightarrow 0^{+}}\ f(x) = \lim_{x ightarrow 0^{+}}\ \lambda\lbrack xbrack = 0$
$\lim_{x ightarrow 0^{-}}\ \ f(x) = \lim_{x ightarrow 0^{-}}\ \ 5^{1/x} = 0$
And $f(0) = \lambda\lbrack 0brack = 0$
$	herefore\ f$ is continuous only whatever $\lambda$ may be

Q. Let $f(x) = \left\{ \begin{array}{r} 5^{1/x},\ \ x < 0 \\ \lambda\lbrack x\rbrack,\ \ \ \ x \geq 0 \end{array} \right.\$ and $\lambda \in R$, then at $x = 0$

Explanation

Reviewed by Dr. Abubacker

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