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Math Help - Use differentials to estimate the value of 30^(1/5)

  1. #1
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    Use differentials to estimate the value of 30^(1/5)

    i know you need to find a nice number that would solve out but the only one i could find was 5 so 5^1/5 = 1. but when i try to put that value into the derivative (1/5)(5^-4/5) i get some random number so i must be doing something wrong! help??
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  2. #2
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    Quote Originally Posted by yess View Post
    i know you need to find a nice number that would solve out but the only one i could find was 5 so 5^1/5 = 1. but when i try to put that value into the derivative (1/5)(5^-4/5) i get some random number so i must be doing something wrong! help??
    f(x + h) \approx f(x) + h f'(x).

    Take f(x) = x^{1/5}, x = 32, h = -2.
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  3. #3
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    Or, you could just use the Binomial expansion.

    30^{1/5}=(32-2)^{1/5}=32^{1/5}(1-2/32)^{1/5}=2(1-1/16)^{1/5} and so on.
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