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Exercise

$\lim_{x\to2}x+1x-5$

Step-by-step Solution

1

Any expression multiplied by $1$ is equal to itself

$\lim_{x\to2}\left(x+x-5\right)$
2

Combining like terms $x$ and $x$

$\lim_{x\to2}\left(2x-5\right)$
3

Evaluate the limit $\lim_{x\to2}\left(2x-5\right)$ by replacing all occurrences of $x$ by $2$

$2\cdot 2-5$
4

Multiply $2$ times $2$

$4-5$
5

Subtract the values $4$ and $-5$

$-1$

Final answer to the exercise

$-1$

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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$\lim_{x\to8}\left(\frac{x-8}{x^2-64}\right)$

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$\lim_{x\to4}\left(\frac{2-\sqrt{x}}{4-x}\right)$

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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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