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anonymous

  • 4 years ago

hey guys i need help solving this limit problem, i know the answer is .25 but i dont know how to show that algebraically i will upload the equation

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  1. anonymous
    • 4 years ago
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  2. anonymous
    • 4 years ago
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    oh and i cant use hospitals rule

  3. Zarkon
    • 4 years ago
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    multiply top and bottom by \[\sqrt{4+x^5}+2\]

  4. anonymous
    • 4 years ago
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    are you sure it is +x^5?

  5. Zarkon
    • 4 years ago
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    yes

  6. Zarkon
    • 4 years ago
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    the only sign change you need in the one in front of the 2

  7. Zarkon
    • 4 years ago
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    from - to +

  8. anonymous
    • 4 years ago
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    well that leaves me with 0/0 which is indeterminate form which is bad

  9. Zarkon
    • 4 years ago
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    \[(\sqrt{4+x^5}-2)(\sqrt{4+x^5}+2)=4+x^5-4=x^5\] then cancel the \(x^5\) that is in the numerator and the denominator

  10. Zarkon
    • 4 years ago
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    then take limit

  11. Zarkon
    • 4 years ago
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    \[\lim_{x\to 0}\frac{\sqrt{4+x^5}-2}{x^5}\] \[\lim_{x\to 0}\frac{\sqrt{4+x^5}-2}{x^5}\frac{\sqrt{4+x^5}+2}{\sqrt{4+x^5}+2}\] \[\lim_{x\to 0}\frac{x^5}{x^5(\sqrt{4+x^5}+2)}\] \[\lim_{x\to 0}\frac{1}{\sqrt{4+x^5}+2}\] \[\lim_{x\to 0}\frac{1}{\sqrt{4}+2}=\frac{1}{4}\]

  12. anonymous
    • 4 years ago
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    oh ok makes i see now thanks

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