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Exercise

$\lim_{x\to2}\left(\frac{x^2-1}{\sqrt{x}-1}\right)$

Step-by-step Solution

1

Evaluate the limit $\lim_{x\to2}\left(\frac{x^2-1}{\sqrt{x}-1}\right)$ by replacing all occurrences of $x$ by $2$

$\frac{2^2-1}{\sqrt{2}-1}$
2

Calculate the power $2^2$

$\frac{4-1}{\sqrt{2}-1}$
3

Subtract the values $4$ and $-1$

$\frac{3}{\sqrt{2}-1}$

Final answer to the exercise

$\frac{3}{\sqrt{2}-1}$

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

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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