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Exercise

$\lim_{x\to-2}\left(\frac{\sqrt{x+5}}{x-1}\right)$

Step-by-step Solution

1

Evaluate the limit $\lim_{x\to-2}\left(\frac{\sqrt{x+5}}{x-1}\right)$ by replacing all occurrences of $x$ by $-2$

$\frac{\sqrt{-2+5}}{-2-1}$
2

Subtract the values $-2$ and $-1$

$\frac{\sqrt{-2+5}}{-3}$
3

Subtract the values $5$ and $-2$

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

Rewrite the fraction with the minus sign in the numerator

$\frac{0}{3}$
5

Divide $0$ by $3$

0

Final answer to the exercise

0

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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