# Thread: Limits with substitution

1. ## Limits with substitution

Okay, I just started AP Calc at school and I'm confused about how to determine limits by substitution and to support it graphically. I know this is probably really simple but I need help.

Problem: lim 3x^2(2x+1)
x approaches -1/2

Problem #2: lim e^x cos x
x approaches 0

Thanks for your help, ahead of time!

2. Originally Posted by Jasmina8
Okay, I just started AP Calc at school and I'm confused about how to determine limits by substitution and to support it graphically. I know this is probably really simple but I need help.

Problem: lim 3x^2(2x+1)
x approaches -1/2

Problem #2: lim e^x cos x
x approaches 0

Thanks for your help, ahead of time!
Hi Jasmina8.

Substitution is the easiest way to find limits, so that's good. Substitution means that you simply substitute the value x approaches for x in your function/expression and see what value you get. For a lot of basic expressions, this value is the limit you want to find.

What do you get when you plug in -1/2 for x in the 1st problem? How about 0 in the second?

3. Well for the first one I got -3/2, and for the second one I got 0.

4. Is the first one supposed to be $\displaystyle 3^{x^2(2x+1)}$ or $\displaystyle 3x^{2}(2x+1)$?

I get something different for #2. Please show your work so I can help.