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Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim_(x->7)f(x) text(, where ) f(x)={(x**2-8 x+7 text(if ) x < 7,-x**2 + 8 x - 7 text(if ) x >= 7)

Respuesta :

gmany

Answer:

[tex]\large\boxed{\lim\limits_{x\to7}f(x)=0}[/tex]

Step-by-step explanation:

[tex]f(x)=\left\{\begin{array}{ccc}x^2-8x+7&if&x<7\\-x^2+8x-7&if&x\geq7\end{array}\right\\\\\lim\limits_{x\to7}f(x)=?\\\\\lim\limits_{x\to7^-}(x^2-8x+7)=7^2-(8)(7)+7=49-56+7=0\\\\\lim\limits_{x\to7^+}(-x^2+8x-7)=-7^2+(8)(7)-7=-49+56-7=0\\\\\lim\limits_{x\to7^-}=\lim\limits_{x\to7^+}=0\Rightarrow\lim\limits_{x\to7}f(x)=0[/tex]

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