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Math Help - Determine following limit: lim x->2 x/(x+2)?

  1. #1
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    Determine following limit: lim x->2 x/(x+2)?

    Determine following limit: lim x->2 x/(x+2)?

    dont know how to go about this one, i know the answer is 1/2 but im not too sure how to go get this answer, could someone show full working, cheers!
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  2. #2
    Super Member TheChaz's Avatar
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    Quote Originally Posted by hellomoto89 View Post
    Determine following limit: lim_ {x \to 2} \frac{x}{x+2}?

    dont know how to go about this one, i know the answer is 1/2 but im not too sure how to go get this answer, could someone show full working, cheers!
    Direct substitution. Just replace x with 2.
    This fails frequently, but I'm sure you'll let us know when you get to that bridge!
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  3. #3
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    There are four basic "rules" for limits:
    1) If \lim_{x\to a} f(x)= F and \lim_{x\to a} g(x)= G then \lim_{x\to a} f(x)+ g(x)= F+ G
    2) If \lim_{x\to a} f(x)= F and \lim_{x\to a} g(x)= G then \lim_{x\to a}f(x)g(x)= FG
    3) If \lim_{x\to a} f(x)= F and \lim_{x\to a} g(x)= G, and G\ne 0, then \lim_{x\to a} \frac{f(x)}{g(x)}= \frac{F}{G}.
    4) If f(x)= g(x) for all x except x= a, then \lim_{x\to a}f(x)= \lim_{x\to a}g(x).

    Here, (3) applies.

    It's when G= 0 that (3) does not apply, as TheChas said, and then you often can use (4).

    You also, of course, need to know the "trivial" limits:
    \lim_{x\to a} C= C where C is a constant.
    \lim_{x\to a} x= a.
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