Find the limit of $\frac{\sqrt[3]{x}-1}{\sqrt[4]{x}-1}$ as $x$ approaches $1$

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Final answer to the problem

indeterminate

Step-by-step Solution

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  • Solve without using l'Hôpital
  • Solve using L'Hôpital's rule
  • Solve using limit properties
  • Solve using direct substitution
  • Solve the limit using factorization
  • Solve the limit using rationalization
  • Integrate by partial fractions
  • Product of Binomials with Common Term
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1

Evaluate the limit $\lim_{x\to1}\left(\frac{\sqrt[3]{x}-1}{\sqrt[4]{x}-1}\right)$ by replacing all occurrences of $x$ by $1$

$\frac{\sqrt[3]{1}-1}{\sqrt[4]{1}-1}$

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$\frac{\sqrt[3]{1}-1}{\sqrt[4]{1}-1}$

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Learn how to solve problems step by step online. Find the limit of (x^(1/3)-1)/(x^(1/4)-1) as x approaches 1. Evaluate the limit \lim_{x\to1}\left(\frac{\sqrt[3]{x}-1}{\sqrt[4]{x}-1}\right) by replacing all occurrences of x by 1. Calculate the power \sqrt[4]{1}. Subtract the values 1 and -1. Calculate the power \sqrt[3]{1}.

Final answer to the problem

indeterminate

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Plotting: $\frac{\sqrt[3]{x}-1}{\sqrt[4]{x}-1}$

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