Question

limx->-4 (sqrt(x^2+9)-5)/x+4

Answer 1

the -5 is out of the sqrt

Answer 2

would the answer be -4-8/-4+4 = 0?

Answer 3

i mean undefined

Answer 4

the question is evaluate the limit. no tables allowed

Answer 5

heard of `rationalizing` before ?

Answer 6

\[\large \lim\limits_{x\to -4}\dfrac{\sqrt{x^2+9}-5}{x+4}\]

Answer 7

like that ?

Answer 8

yeah

Answer 9

oh i see now do i have to multiply by sqrt(x^2+9)+5 top and bottom?

Answer 10

multiply by 1 : \[\large \dfrac{\sqrt{x^2+9}+5}{\sqrt{x^2+9}+5}\]

Answer 11

yes you're right!

Answer 12

ok let me work on it

Answer 13

so i got 1/sqrt(5)+5 i think i did something wrong

Answer 14

i think i saw my mistake i forgot to multiply the -5*5

Answer 15

oh crap i also made a typo i forgot to write x^2

Answer 16

\[\large \begin{align} \lim\limits_{x\to -4}\dfrac{\sqrt{x^2+9}-5}{x+4}&= \lim\limits_{x\to -4}\dfrac{\sqrt{x^2+9}-5}{x+4} \times \dfrac{\sqrt{x^2+9}+5}{\sqrt{x^2+9}+5} \\~\\&=\lim\limits_{x\to -4} \dfrac{\left(\sqrt{x^2+9}\right)^2-5^2}{\left(x+4\right)\left(\sqrt{x^2+9}+5\right)}\\~\\ &= \lim\limits_{x\to -4} \dfrac{x^2+9-25}{\left(x+4\right)\left(\sqrt{x^2+9}+5\right)}\\~\\ &= \lim\limits_{x\to -4} \dfrac{x^2-16}{\left(x+4\right)\left(\sqrt{x^2+9}+5\right)}\\~\\ &= \lim\limits_{x\to -4} \dfrac{(x-4)(x+4)}{\left(x+4\right)\left(\sqrt{x^2+9}+5\right)}\\~\\ &= \lim\limits_{x\to -4} \dfrac{x-4}{\sqrt{x^2+9}+5}\\~\\ \end{align}\]

Answer 17

take the limit now

Answer 18

i got -4/15

Answer 19

no i meant -4/5