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Exercise

$\lim_{x\to0}\left(\frac{\sqrt{5+x}-\sqrt{5}}{x+2}\right)$

Step-by-step Solution

1

Evaluate the limit $\lim_{x\to0}\left(\frac{\sqrt{5+x}-\sqrt{5}}{x+2}\right)$ by replacing all occurrences of $x$ by $0$

$\frac{\sqrt{5+0}-\sqrt{5}}{0+2}$
2

Add the values $0$ and $2$

$\frac{\sqrt{5+0}-\sqrt{5}}{2}$
3

Add the values $5$ and $0$

$\frac{\sqrt{5}-\sqrt{5}}{2}$
4

Cancel like terms $\sqrt{5}$ and $-\sqrt{5}$

$\frac{0}{2}$
5

Divide $0$ by $2$

0

Final answer to the exercise

0

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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