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Find the limit of $\frac{1-\cos\left(x\right)}{x^2}$ as $x$ approaches 0

Step-by-step Solution

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asinh
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Final answer to the problem

indeterminate

Step-by-step Solution

How should I solve this problem?

  • Solve using direct substitution
  • Solve using L'Hôpital's rule
  • Solve without using l'Hôpital
  • Solve using limit properties
  • Solve the limit using factorization
  • Solve the limit using rationalization
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
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1

Evaluate the limit $\lim_{x\to0}\left(\frac{1-\cos\left(x\right)}{x^2}\right)$ by replacing all occurrences of $x$ by $0$

$\frac{1-\cos\left(0\right)}{0^2}$
2

Calculate the power $0^2$

$\frac{1-\cos\left(0\right)}{0}$
3

The cosine of $0$ equals

$\frac{1-1}{0}$
4

Subtract the values $1$ and $-1$

$\frac{0}{0}$
5

$\frac{0}{0}$ represents an indeterminate form

indeterminate

Final answer to the problem

indeterminate

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Function Plot

Plotting: $\frac{1-\cos\left(x\right)}{x^2}$

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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