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Math Help - Using limits to find other limits

  1. #1
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    Using limits to find other limits

    Hello everyone,
    I am not completely sure of how to approach this problem:

    If lim f(x)/x^2 as x-->0 is equal to 5, find the following limits:

    a) lim f(x) as x--> 0
    b) lim f(x)/x as x--> 0

    Any suggestions would be appreciated.
    Thank you !
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  2. #2
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    Quote Originally Posted by zeda234 View Post
    Hello everyone,
    I am not completely sure of how to approach this problem:

    If lim f(x)/x^2 as x-->0 is equal to 5, find the following limits:

    what would f(x) have to be for the above limit to be true?

    a) lim f(x) as x--> 0
    b) lim f(x)/x as x--> 0
    ...
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  3. #3
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    Quote Originally Posted by skeeter View Post
    ...
    Thanks for your reply.
    So in order for the statement to be true, it is necessary to eliminate the x^2 in the denominator right? Otherwise you would be dividing by zero. So could f(x) be 5(x^2)? This way the x^2 would divide out and 5 would be left?
    Am I on the right track?
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  4. #4
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    Quote Originally Posted by zeda234 View Post
    Thanks for your reply.
    So in order for the statement to be true, it is necessary to eliminate the x^2 in the denominator right? Otherwise you would be dividing by zero. So could f(x) be 5(x^2)? This way the x^2 would divide out and 5 would be left?
    Am I on the right track?
    ... keep going
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  5. #5
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    Quote Originally Posted by skeeter View Post
    ... keep going
    Ok. So...

    (a) lim 5(x^2) as x-->0
    The answer is zero then?

    (b)lim 5(x^2)/x as x-->0
    The answer is also zero?

    So then both answers are zero?
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  6. #6
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    Quote Originally Posted by zeda234 View Post
    Ok. So...

    (a) lim 5(x^2) as x-->0
    The answer is zero then?

    (b)lim 5(x^2)/x as x-->0
    The answer is also zero?

    So then both answers are zero?
    you figure out what f(x) must be on your own ... why then do you doubt your solutions to these two simple limits?
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  7. #7
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    Quote Originally Posted by skeeter View Post
    you figure out what f(x) must be on your own ... why then do you doubt your solutions to these two simple limits?
    The textbook I have used a different method for a similar question earlier on and it looks far more complicated. So I just wasn't sure if guessing was correct. Therefore, both answers are indeed zero right?
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  8. #8
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    yes.
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