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Exercise

$\lim_{x\to16\:}\frac{\sqrt{x-4}}{\sqrt[4]{x-2}}$

Step-by-step Solution

1

Evaluate the limit $\lim_{x\to16}\left(\frac{\sqrt{x-4}}{\sqrt[4]{x-2}}\right)$ by replacing all occurrences of $x$ by $16$

$\frac{\sqrt{16-4}}{\sqrt[4]{16-2}}$
2

Subtract the values $16$ and $-2$

$\frac{\sqrt{16-4}}{\sqrt[4]{14}}$
3

Subtract the values $16$ and $-4$

$\frac{\sqrt{12}}{\sqrt[4]{14}}$

Final answer to the exercise

$\frac{\sqrt{12}}{\sqrt[4]{14}}$

Try other ways to solve this exercise

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  • 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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$\lim_{x\to-4}\left(\frac{x+4}{x^2-16}\right)$

Main Topic: Limits by Direct Substitution

Find limits of functions at a specific point by directly plugging the value into the function.

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