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Homework Help: Limits problem

  1. Feb 10, 2016 #1
    • Member warned about posting without the homework template
    hi I don't understand how to do one type of homework problem, here's an example of the type:
    If limit of f(X)/X = 1 as X ->0 evaluate the limit f(X) as X->0
     
  2. jcsd
  3. Feb 10, 2016 #2
    I realize now that f(X) must equal X and therefor the limit is 0
     
  4. Feb 11, 2016 #3

    Samy_A

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    Science Advisor
    Homework Helper

    That's not a correct argument.

    For example, ##\displaystyle \lim_{x\rightarrow 0} \frac{\sin x}{x}=1##, but clearly ##\sin x \neq x## (for ##x \neq 0##).

    You could use the product rule for limits: ##\displaystyle \lim_{x\rightarrow 0} g(x)h(x)=(\lim_{x\rightarrow 0} g(x))(\lim_{x\rightarrow 0} h(x))## provided the limits exist.
    Notice that ##f(x)=x\frac{f(x)}{x}##.
     
    Last edited: Feb 11, 2016
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