## Related questions with answers

Question

Determine whether each function is (a) continuous from the left. (b) continuous from the right. at the numbers c and d. $f(x)=\sqrt{(x+1)(x-5)}$ at c=-1 and d=5

Solution

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1 of 4$f(x)=\sqrt{(x+1)(x-5)}$

$\lim\limits_{x^{-} \to -1}=\lim\limits_{x^{-} \to -1}\sqrt{(x+1)(x-5)}=complex$

$\lim\limits_{x^{+} \to -1}=\lim\limits_{x^{+} \to -1}\sqrt{(x+1)(x-5)}=real$

Since left and right limits are not equal the given function is not continuous at $c=-1$

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