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

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indeterminate

##  Step-by-step Solution 

How should I solve this problem?

• Solve using limit properties
• Solve using L'Hôpital's rule
• Solve without using l'Hôpital
• 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
• Integrate by substitution
Can't find a method? Tell us so we can add it.
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 $1$

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

Subtract the values $1$ and $-1$

$\frac{0}{0}$
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5

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

indeterminate

indeterminate

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

###  Main Topic: Limits by Direct Substitution

Find limits of functions at a specific point by directly plugging the value into the function.