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Math Help - Help evaluating the limits of these two problems, one of which is a complex fraction

  1. #1
    Newbie dannibambi's Avatar
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    Question Help evaluating the limits of these two problems, one of which is a complex fraction

    I like finding limits, but complex fractions and I do not get along. I would greatly appreciate it if someone could help me evaluate the limits of the following two problems (step-by-step). For #37, I received a different answer from Mathway.com, which was also a different answer from the back of my book, so I am very lost. I appreciate the help!

    Help evaluating the limits of these two problems, one of which is a complex fraction-math-help.jpg

    Thank you!
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  2. #2
    Newbie dannibambi's Avatar
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    Re: Help evaluating the limits of these two problems, one of which is a complex fract

    Actually, I figured out #38 (the formatting threw me off, but it was easy), so I just need help with number #37. Thank you!! :-)
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    Re: Help evaluating the limits of these two problems, one of which is a complex fract

    Hello, dannibambi!

    37.\;\lim_{x\to\text{-}4} \dfrac{\frac{1}{4} + \frac{1}{x}}{x+4}

    Multiply by \frac{4x}{4x}\!: \;\;\dfrac{4x\left(\frac{1}{4} + \frac{1}{x}\right)}{4x(x+4)} \;=\; \frac{x+4}{4x(x+4)} \;=\;\frac{1}{4x}

    Therefore: . \lim_{x\to\text{-}4}\frac{1}{4x} \;=\;-\frac{1}{16}
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    Re: Help evaluating the limits of these two problems, one of which is a complex fract

    Help evaluating the limits of these two problems, one of which is a complex fraction-limit.png
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  5. #5
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    Re: Help evaluating the limits of these two problems, one of which is a complex fract

    Quote Originally Posted by ibdutt View Post
    Click image for larger version. 

Name:	Limit.png 
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    I expect you meant to write "lim" instead of "log"...
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    Re: Help evaluating the limits of these two problems, one of which is a complex fract

    Thank you so much!! I can't believe I over-thought it that much. I was trying to multiply the numerator by 4+x and not multiply the denominator by anything...hence my headache-on-top-of-headache... Thanks!! :-)
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