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Exercise

$\lim_{x\to b}\frac{\sqrt[8]{x}-\sqrt[5]{b}}{\sqrt[3]{b}-\sqrt[7]{x}}$

Step-by-step Solution

1

Evaluate the limit $\lim_{x\to b}\left(\frac{\sqrt[8]{x}-\sqrt[5]{b}}{\sqrt[3]{b}-\sqrt[7]{x}}\right)$ by replacing all occurrences of $x$ by $b$

$\frac{\sqrt[8]{b}-\sqrt[5]{b}}{\sqrt[3]{b}-\sqrt[7]{b}}$

Final answer to the exercise

$\frac{\sqrt[8]{b}-\sqrt[5]{b}}{\sqrt[3]{b}-\sqrt[7]{b}}$

Try other ways to solve this exercise

  • Choose an option
  • Solve using L'Hôpital's rule
  • Solve without using l'Hôpital
  • 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
  • FOIL Method
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Similar Questions Solved

$\int\frac{dx}{x^2+7x-6}$

$\int\frac{dx}{x^2+7x+6}$

Main Topic: Integrals of Rational Functions

Integrals of rational functions of the form R(x) = P(x)/Q(x).

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