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Exercise

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

Step-by-step Solution

1

Factor the difference of squares $x^2-25$ as the product of two conjugated binomials

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

Simplify the fraction $\frac{\left(x+5\right)\left(x-5\right)}{x-5}$ by $x-5$

$x+5$
3

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

$5+5$
4

Add the values $5$ and $5$

$10$

Final answer to the exercise

$10$

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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Main Topic: Limits by Factoring

Limits that require factorization techniques to solve them.

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