Find all values of c such that f is continuous on

Ответ:

meep26wesley

03.01.2022

$f(x)=\begin{cases}5-x^2&\text{for }x\le c\\x&\text{for }xc\end{cases}$

will be continuous as long as

$\displaystyle\lim_{x\to c^-}f(x)=\lim_{x\to c^+}f(x)=f(c)$

We have

$\displaystyle\lim_{x\to c^-}f(x)=\lim_{x\to c}(5-x^2)=5-c^2$

$\displaystyle\lim_{x\to c^+}f(x)=\lim_{x\to c}x=c$

so we must satisfy

$5-c^2=c\implies c^2+c-5=0\implies c=\dfrac{-1\pm\sqrt{21}}2$

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Ответ:

MajentaSnow2613

05.09.2022

Mathematics

step-by-step explanation:

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Find all values of c such that f is continuous on (-∞, ∞). $ f(x) = \left\{ \begin{array}{lcl} {\color{red}5} - x^{2}, & & x \le c \\ x, & & x > c \end{array}\right. $

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