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Exercise

$\lim_{x\to3}\left(x^2-x-6\right)\left(x-3\right)$

Step-by-step Solution

1

Evaluate the limit $\lim_{x\to3}\left(x^2-x-6\right)$ by replacing all occurrences of $x$ by $3$

$\left(3^2-3-6\right)\left(x-3\right)$
2

Subtract the values $-3$ and $-6$

$\left(3^2-9\right)\left(x-3\right)$
3

Calculate the power $3^2$

$\left(9-9\right)\left(x-3\right)$
4

Subtract the values $9$ and $-9$

$0\left(x-3\right)$
5

Any expression multiplied by $0$ is equal to $0$

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

In mathematics, a limit is the value that a function or sequence "approaches" as the input or index approaches some value.

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