Question

Use properties of limits to find the indicated limit. It may be necessary to rewrite an expression before limit properties can be applied.

lim
x -> 0 (2x^2 + 2x + 3)^2

A. -9

B. 9

C. does not exist

D. 1

Answer 1

What problem are you having with this one?

Answer 2

i want to know what is the answer and why

Answer 3

What do know about limits? Do you understand what they are? If not, that is the issue. If so, then it should be pretty easy to do this one, but there may be some other concept issue.

Answer 4

no what are limits...i easily forget things

Answer 5

A limit is basically where things are heading towards, not where they are at, but where they seem to be going to. This is easy with basic polynomials because where they are going to is clear. However, if it is a rational expression, \(\frac{something}{x}\), then it can be harder.

Answer 6

oh ok what do i do first to figure out the answer to this problem

Answer 7

Well, the good news is that this is a simple polynomial. It is a smooth curve that has no holes, jumps, or asymptotes. Because of that, you can just put in the x=0 and see where it is going.

Answer 8

ok let me figure it out

Answer 9

is it B. 9

Answer 10

Yes.

Answer 11

If you want a good reference on limits so you can learn about them some more or if you need to look at other things like one sided limits or one like the over x one, here are some nice notes: http://tutorial.math.lamar.edu/Classes/CalcI/LimitsIntro.aspx

Answer 12

thanks and thank you so much for your time. @e.mccormick

Answer 13

np. Have fun!

Answer 14

;-) @e.mccormick