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anonymous

  • one year ago

lim x -> -4 (1/4 + 1/x)/(4+x) The answer is -1/16 Here is what I did: (1/4 + 1/x)(1/4 + 1/x) 1/16+2/4x+1/x^2 1/16+2/4(-4)+1/(-4)^2 1/16-2/16+1/16 0

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  1. anonymous
    • one year ago
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    I know this guy solved it: https://www.youtube.com/watch?v=9_RUnj-5wEk, but I don't get why my technique doesn't work.

  2. anonymous
    • one year ago
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    @Hero

  3. Hero
    • one year ago
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    \(\begin{align*}\dfrac{\dfrac{1}{4} + \dfrac{1}{x}}{4 + x} &= \left(\dfrac{1}{4} + \dfrac{1}{x}\right) \div (4 + x) \\&= \left(\dfrac{x}{4x} + \dfrac{4}{4x}\right) \div (4 + x) \\&= \left(\dfrac{x + 4}{4x} \times \dfrac{1}{x + 4}\right)\\&=\dfrac{1}{4x}\end{align*}\) \(\lim_{x \to -4}\dfrac{1}{4x} = \dfrac{1}{4(-4)} = -\dfrac{1}{16}\)

  4. anonymous
    • one year ago
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    Thank you! But, I was more wondering why my answer didn't work... because, I know there is something wrong about it, but I can't spot what.

  5. ytrewqmiswi
    • one year ago
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    Are these 2 equal- 1/(4+x) and (1/4+1/x)

  6. ytrewqmiswi
    • one year ago
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    I think u made a mistake in the 1st step

  7. Hero
    • one year ago
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    @vvbb you can discover what you did wrong for yourself.

  8. anonymous
    • one year ago
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    Can't I use this formula for the first step? (a/b)/(c/d)=(a/b)*(c/d)

  9. Hero
    • one year ago
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    You shouldn't use that formula and what you just posted demonstrates why. Instead use this: \(\dfrac{\dfrac{a}{b}}{\dfrac{c}{d}} = \dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{a}{b} \times \dfrac{d}{c}\)

  10. anonymous
    • one year ago
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    okay

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spraguer (Moderator)
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