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Exercise

$\lim_{x\to0}\left(\left(3x^3+2\right)^2\right)$

Step-by-step Solution

1

Evaluate the limit $\lim_{x\to0}\left(\left(3x^3+2\right)^2\right)$ by replacing all occurrences of $x$ by $0$

$\left(3\cdot 0^3+2\right)^2$
2

Calculate the power $0^3$

$\left(3\cdot 0+2\right)^2$
3

Multiply $3$ times $0$

$\left(0+2\right)^2$
4

Add the values $0$ and $2$

$2^2$
5

Calculate the power $2^2$

$4$

Final answer to the exercise

$4$

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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