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Exercise

$\lim_{x\to-3}\left(3x^2+5x\right)$

Step-by-step Solution

1

Evaluate the limit $\lim_{x\to-3}\left(3x^2+5x\right)$ by replacing all occurrences of $x$ by $-3$

$3\cdot {\left(-3\right)}^2+5\cdot -3$
2

Multiply $5$ times $-3$

$3\cdot {\left(-3\right)}^2-15$
3

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

$3\cdot 9-15$
4

Multiply $3$ times $9$

$27-15$
5

Subtract the values $27$ and $-15$

$12$

Final answer to the exercise

$12$

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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