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Exercise

$\lim_{x\to4}\left(-\frac{3x}{x-2}\right)$

Step-by-step Solution

1

Evaluate the limit $\lim_{x\to4}\left(\frac{-3x}{x-2}\right)$ by replacing all occurrences of $x$ by $4$

$\frac{-3\cdot 4}{4-2}$
2

Subtract the values $4$ and $-2$

$\frac{-3\cdot 4}{2}$
3

Multiply $-3$ times $4$

$-\frac{12}{2}$
4

Divide $-12$ by $2$

$-6$

Final answer to the exercise

$-6$

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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