Question

How do I find the limit of (x+3)^2 if x is approaching negative 4?

Answer 1

This is a polynomial, so you can use direct substitution. Plug in -4 for x

Answer 2

So,
((-4)+3)^2

Answer 3

yes

Answer 4

No foiling is required for the polynomial before plugging it in?

Answer 5

you can, but it's not necessary. You'll get the same value regardless

Answer 6

Okay, I just wanted to make sure I wasn't doing unnecessary steps. May I ask another quick question?

Answer 7

ok

Answer 8

If I'm just finding the limit, I just plug the value x is approaching into the limit.
So, for the limit (x/(x^2+4)) with x approaching 1. I would just plug in the value of 1 for x without any other steps?

Answer 9

yes you can just plug in for that limit, but that doesn't always work, especially for rational functions

Answer 10

so sometimes you will have to factor or do some other type of algebra, but it really depends on the function and the value of x it's approaching

Answer 11

Do you perhaps have an example of when factoring would be required?

Answer 12

\[\lim_{x \rightarrow -2}\frac{ x+2 }{ x^2-4 }\]
Plugging in -2 makes the denominator be 0.
\[\lim_{x \rightarrow -2}\frac{ x+2 }{ (x+2)(x-2) }\]
Cancel
\[\lim_{x \rightarrow -2}\frac{ 1 }{ (x-2) }\]
Now plug in to get \(-\frac{ 1 }{ 4 }\)

Answer 13

I have a problem right now that wishes for me to write a simpler function that agrees with the given function at all but one point. Then to find the limit of that function.
The limit as x approaches 0 of the limit (x^2+3x)/x.

Answer 14

I'm not entirely sure what they mean by a simpler function, unless they would like me to factor out the x values to cancel out the x's.

Answer 15

do you know what a piecewise function is?

Answer 16

I haven't used a piecewise function in awhile, if you could explain it to me, I'd very much appreciate it.

Answer 17

the ones that look like this, with two different functions for different parts of the domain