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ext{Lim}_{x \rightarrow $0$ }\cos( $4$ x) $-1$

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Solve multi-step inequalities

Full solution

Q. ext{Lim}_{x \rightarrow

0

}\cos(

4

x)

-1

Apply Limit Properties: To solve the limit of $\cos(4x) - 1$ as $x$ approaches $0$ , we can use the limit properties and the fact that the limit of $\cos(x)$ as $x$ approaches $0$ is $1$ .
Find Limit of $-1$ : We know that the limit of a constant is the constant itself, so the limit of $-1$ as $x$ approaches $0$ is $-1$ .
Substitute $x$ with $0$ : Now, we need to find the limit of $\cos(4x)$ as $x$ approaches $0$ . Since the cosine function is continuous everywhere, we can directly substitute the value of $x$ with $0$ in $\cos(4x)$ .
Calculate $\cos(0)$ : Substituting $x$ with $0$ in $\cos(4x)$ gives us $\cos(0)$ , which is equal to $1$ .
Combine Limits: Now, we combine the limits of $\cos(4x)$ and $-1$ . Since the limit of $\cos(4x)$ as $x$ approaches $0$ is $1$ , and the limit of $-1$ is $-1$ , we have: $\newline$ Limit as $x$ approaches $0$ of $-1$ $0$ .
Calculate Final Result: Calculating $1 - 1$ gives us $0$ .

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