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anonymous

  • 5 years ago

Find the lim x->4 of ((x^1/2)-2)/(x-4)

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  1. watchmath
    • 5 years ago
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    Are we allowed to use L'Hospital rule?

  2. anonymous
    • 5 years ago
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    yes.

  3. anonymous
    • 5 years ago
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    i have the answer i just dont know how to get there.

  4. watchmath
    • 5 years ago
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    Then you just need to differentiate the top and the bottom and then compute the limit.

  5. anonymous
    • 5 years ago
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    yeah im completely stuck and dont understand it.

  6. watchmath
    • 5 years ago
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    $$\lim_{x\to 4} \frac{\sqrt{x}-2}{x-4}=\lim_{x\to 4}\frac{\frac{1}{2}x^{-1/2}}{1}=\frac{1}{4}$$

  7. anonymous
    • 5 years ago
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    thanks!

  8. anonymous
    • 5 years ago
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    Can also solve this one with conjugate of (sqrt x) -2 multiply top and bottom by (sqrt x) +2 that will eventually get you ((sqrt x)-2)^2 in the numerator which equals x-4 x-4's cancel giving you 1/(sqrt x) =2 in denominator : substitute limit 1/(2+2) = 1/4

  9. watchmath
    • 5 years ago
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    That's correct! :D

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