f(x)={1+((√x^2 )/x) if x#0 2 if x=0 study the continuty of f in 0


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Question Number 203291 by zahaku last updated on 14/Jan/24
$f(x)={1+((√x^2 )/x) if x#0 2 if x=0 study the continuty of f in 0$
$You can't use 'macro parameter character #' in math mode$ $2 i f x = 0$ $s t u d y t h e c o n t i n u t y o f f i n 0$
	Answered by esmaeil last updated on 15/Jan/24
	$f(x)= { ((1+((∣x∣)/x) if x≠0)),((2 if x=0)) :} lim_(x→0^+ ) f(x)=1+1=2=f(0) lim_(x→0^− ) f(x)=1−1=0≠f(0) →not continuty$
	$f (x) = {\begin{cases} 1 + \frac{∣ x ∣}{x} i f x \neq 0 \\ 2 i f x = 0 \end{cases}$ $\lim_{x \to 0^{+}} f (x) = 1 + 1 = 2 = f (0)$ $\lim_{x \to 0^{-}} f (x) = 1 - 1 = 0 \neq f (0)$ $\to n o t c o n t i n u t y$
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