Question

`lim_(xrarr-3)(x+3)/(4-sqrt(2x+22))` by using L'Hôpital's Rule?

Answer 1

The limit equals `-4`.

Explanation:

If we try evaluating into the initial expression, we get

`L = 0/0 = oo`

So we can use l'Hopitals Rule.

`L = lim_(x->-3) 1/( - 2/(2sqrt(2x + 22)))`

`L = lim_(x->-3) 1/(- 1/sqrt((2x + 22))`

`L = lim_(x-> -3) -sqrt(2x + 22)`

Now we can evaluate directly:

`L = -sqrt(2(-3) + 22)`

`L = -sqrt(16)`

`L = -4`

If we do a graphical check, we obtain the same result.

graph{(x + 3)/(4 - sqrt(2x + 22)) [-10, 10, -5, 5]}

Hopefully this helps!