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Math Help - Approximation using Taylor's Theorem

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    Approximation using Taylor's Theorem

    If x>0 show that |(1+x)^{1/3}-(1+\frac{1}{3}x-\frac{1}{9}x^2)|\leq (5/81)x^3 .
    Use this inequality to approximate \sqrt[3]{1.2} and \sqrt[3]{2} .
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Kipster1203 View Post
    If x>0 show that |(1+x)^{1/3}-(1+\frac{1}{3}x-\frac{1}{9}x^2)|\leq (5/81)x^3 .
    Use this inequality to approximate \sqrt[3]{1.2} and \sqrt[3]{2} .
    Apply Taylor's formula and look at the remainder term. Report back if you have any issues.
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