How do you find the limit of $sqrt(x+1)/(x-4)$ as x approaches 3?

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Answer 1 · 2015-07-15T17:57:50

$lim_{xto3}sqrt(x+1)/(x-4) = -2$

Let's try direct substitution.

$sqrt(x+1)/(x-4) = sqrt(3+1)/(3-4) = sqrt4/(-1)= 2/(-1) = -2$

So the function is continuous at $x = 3$ .

$lim_{xto3}sqrt(x+1)/(x-4) = -2$

How do you find the limit of sqrt(x+1)/(x-4)sqrt(x+1)/(x-4) as x approaches 3?