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Exercise

$\lim_{x\to0}\left(\frac{xsin\left(0\right)}{x^2}\right)$

Step-by-step Solution

1

The sine of $0$ equals $0$

$\lim_{x\to0}\left(\frac{0x}{x^2}\right)$
2

Any expression multiplied by $0$ is equal to $0$

$\lim_{x\to0}\left(\frac{0}{x^2}\right)$
3

Zero divided by anything is equal to zero

$\lim_{x\to0}\left(0\right)$
4

The limit of a constant is just the constant

0

Final answer to the exercise

0

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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Similar Questions Solved

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$\lim_{x\to1}\left(\frac{x^3-1}{4x^3-x-3}\right)$

$\lim_{x\to8}\left(\frac{x-8}{x^2-64}\right)$

$\lim_{x\to3}\left(\frac{x^3-27}{x^2-9}\right)$

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

$\lim_{x\to2}\left(\frac{x^4-16}{x-2}\right)$

$\lim_{x\to-4}\left(\frac{x+4}{x^2-16}\right)$

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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