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Math Help - One sided limits?

  1. #1
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    One sided limits?

    Find the limit if it exists

    1. As delta x approaches 0 limit from the left

    ((1/x+delta(x)-(1/x))/((delta(x))

    2. This second limit is kind of confusing

    As x approaches 3

    where f(x)=

    (x+2)/2 x < or equal to 3

    12-2x/3 x>3

    Would I just plug in 3+2/2=2.5?
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  2. #2
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    Re: One sided limits?

    Quote Originally Posted by homeylova223 View Post
    Find the limit if it exists
    1. As delta x approaches 0 limit from the left
    ((1/x+delta(x)-(1/x))/((delta(x))
    Is this the problem \displaystyle\lim _{\delta x \to 0^ -  } \dfrac{{\frac{1}{{x + \delta x}} - \frac{1}{x}}}{{\delta x}}~?

    Please learn to post readable questions.
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  3. #3
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    Re: One sided limits?

    Yes it is like that. I should learn that latex.
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    Re: One sided limits?

    Determine for the fractions in the numerator a common denominator.
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    Re: One sided limits?

    Quote Originally Posted by homeylova223 View Post
    Yes it is like that. I should learn that latex. PLEASE DO
    \frac{{\frac{1}{{x + \delta x}} - \frac{1}{x}}}{{\delta x}} =  - \frac{{\delta x}}{{\delta x\left[ {x\left( {x + \delta x} \right)} \right]}}
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    Re: One sided limits?

    Quote Originally Posted by homeylova223 View Post
    Find the limit if it exists

    1. As delta x approaches 0 limit from the left

    ((1/x+delta(x)-(1/x))/((delta(x))

    [snip]
    This has the form of a derivative from first principles, where f(x) = ...... and so the answer is f'(x) = ......

    Quote Originally Posted by homeylova223 View Post
    Find the limit if it exists

    [snip]

    2. This second limit is kind of confusing

    As x approaches 3

    where f(x)=

    (x+2)/2 x < or equal to 3

    12-2x/3 x>3

    Would I just plug in 3+2/2=2.5?
    The right hand limit is 12 - 2(3)/3 = .... and the left hand limit is (3 + 2)/2 = ....

    If right and left hand limits are the same then the limit exists and is equal to .... If right and left hand limits are not the same then the limit does not exist.
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