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Find the limit $\lim_{x\to0}\left(\frac{1-\cos\left(x\right)}{x^2}\right)$

Step-by-step Solution

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Final Answer

indeterminate

Step-by-step Solution

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We could not solve this problem by using the method: Limits by Factoring

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 $-1$

$\frac{0}{0}$
5

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

indeterminate

Final Answer

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

Limits by Direct SubstitutionLimits by L'Hôpital's ruleLimits by Rationalizing

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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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