Question

Evaluating limits (show algebraically)

Answer 1

ok so the original actually was as x approaches -infinity
does that change the whole thing? D:

Answer 2

I forgot to notice that :/ the question is
"Evaluate the following limit. Give more than an answer, show the process you would use to algebraically evaluate the limit"
\[\lim_{x \rightarrow infinity} \sqrt{16x^2+x}-4\]

Answer 3

oh gosh *NEGATIVE infinity

Answer 4

\[\lim_{x \rightarrow -\infty} \sqrt{16x^2+x}-4x\] this right, that should be infinity then

Answer 5

i'll say it changes

Answer 6

you get \[\infty+\infty=\infty\]

Answer 7

Yup

Answer 8

Blegh. how do I solve this then .-.

Answer 9

You don't have to do that tedious math :P

Answer 10

I have to show it algebraically though

Answer 11

Why are you multiplying by the conjugate and stuff?

Answer 12

This one is simple, just plug and chug

Answer 13

really? D:

Answer 14

like for example this is the first one he had us do: [if you can check it to that would be awesome xP]

Answer 15

hmm hm ok. I think it's because he put this one under the same question that I just assumed i should do that

Answer 16

Is it suppose to be \(\rm \infty\) or \(\rm -\infty\) for this limit you're working on? :d
because it makes a big difference.

Answer 17

Oh wait, if you have + infinity then you would do all that

Answer 18

-infinity

Answer 19

Ok you're good :P

Answer 20

it's -infinity and i did it for infinity so it got all bad hahah

Answer 21

If it was + infinity you would have 1/8

Answer 22

well yay! but it's - infinity xD
[was the other one good? the one i just sent]

Answer 23

Yeah, your other one is good as it's approaching +infinity

Answer 24

excellent.
okay so for this one with the -infinty and square root..what?

Answer 25

You don't need to do algebra because it's just infinity + infinity = infinity haha, the other one where it was going towards infinity, you would've had infinity - infinity if you just plug it in, which is uhhh what?! 0! wait no Infinity? That's not right, so you did the algebra :)

Answer 26

Infinity - infinity is undefined

Answer 27

And for the one approaching to - infinity, you have \[\sqrt{\infty}-(-\infty) = \infty \]

Answer 28

that's some shady stuff man xD

Answer 29

Well at least you know why you did the algebra and when not to do it!

Answer 30

Welp. yay!! thanks so much xD

Answer 31

Yw :)