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Exercise

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

Step-by-step Solution

1

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

$\frac{0^2+0}{\left|0\right|}$
2

Calculate the power $0^2$

$\frac{0+0}{\left|0\right|}$
3

Add the values $0$ and $0$

$\frac{0}{\left|0\right|}$
4

Zero divided by anything is equal to zero

0

Final answer to the exercise

0

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

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

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

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

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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