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Math Help - Limits with substitution

  1. #1
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    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!
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  2. #2
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    Quote Originally Posted by Jasmina8 View Post
    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?
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  3. #3
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    Well for the first one I got -3/2, and for the second one I got 0.
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  4. #4
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    Is the first one supposed to be 3^{x^2(2x+1)} or 3x^{2}(2x+1)?

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