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Exercise

$\lim_{x\to2}\left(\frac{3x^2-6x}{x-2}\right)$

Step-by-step Solution

1

Factor the polynomial $3x^2-6x$ by it's greatest common factor (GCF): $3x$

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

Simplify the fraction $\frac{3x\left(x-2\right)}{x-2}$ by $x-2$

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

Evaluate the limit $\lim_{x\to2}\left(3x\right)$ by replacing all occurrences of $x$ by $2$

$3\cdot 2$
4

Multiply $3$ times $2$

$6$

Final answer to the exercise

$6$

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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