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Exercise

$\lim_{x\to-2}\left(12x^3-13\right)$

Step-by-step Solution

1

Evaluate the limit $\lim_{x\to-2}\left(12x^3-13\right)$ by replacing all occurrences of $x$ by $-2$

$12\cdot {\left(-2\right)}^3-13$
2

Calculate the power ${\left(-2\right)}^3$

$12\cdot -8-13$
3

Multiply $12$ times $-8$

$-96-13$
4

Subtract the values $-96$ and $-13$

$-109$

Final answer to the exercise

$-109$

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

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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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