Question

I'm not sure how to start this problem. Limit question is in the comments

Answer 1

epsilon delta again ?

Answer 2

conjugateeee

Answer 3

No just evaluating the limit. I'm not sure if I can take the square root of that with the -5 on there.

Answer 4

try rationalizing the numerator by multiplying top and bottom by conjugate

Answer 5

conjugate is something which when you add/multiply kills the radical

Answer 6

\[\lim_{x \rightarrow -4} \frac{ \sqrt{x^2+9}-5 }{ x+4 } \times \frac{ \sqrt{x^2+9}+5 }{ \sqrt{x^2+9}+5 }\]

Answer 7

Like ganeshie said it's going to kill the numerator at the top because it'll get squared

Answer 8

well its zero by zero form also

Answer 9

l hopital u can use

Answer 10

Have you used L'Hospital before?

Answer 11

l hopital gives the answer fast. we can use it if it is allowed, but the conjugate stuff works pretty nicely too

Answer 12

Yup

Answer 13

I've never heard of a hopital

Answer 14

Np, just use the conjugate and what not, so what did you get using the way we mentioned earlier?

Answer 15

\[\lim_{x \rightarrow -4} \sqrt{x^2+9}+5/(x+4)\]

Answer 16

Mhm well did you do the next step afterwards, that I showed?

Answer 17

It's alright to say you're not sure how to do the next step, we don't judge here, I can show you :)

Answer 18

I think it's \[\lim_{x \rightarrow -4}(x^2+9)^1/2\]