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Exercise

$\lim_{x\to5}\left(\frac{x-5}{x^2+25}\right)$

Step-by-step Solution

1

Evaluate the limit $\lim_{x\to5}\left(\frac{x-5}{x^2+25}\right)$ by replacing all occurrences of $x$ by $5$

$\frac{5-5}{5^2+25}$
2

Subtract the values $5$ and $-5$

$\frac{0}{5^2+25}$
3

Calculate the power $5^2$

$\frac{0}{25+25}$
4

Add the values $25$ and $25$

$\frac{0}{50}$
5

Divide $0$ by $50$

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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