(54) lim_(x rarr0)(cos(4x))/(cos(2x))

Given Limit Expression: We are given the limit expression: lim_(x -> 0)(cos(4x))/(cos(2x)) To solve this limit, we will directly substitute the value of x as 0, since cos(4x) and cos(2x) are continuous functions and there is no indeterminate form.Substitute x = 0: Substitute x = 0 into the expression: (cos(4*0))/(cos(2*0))Simplify Using cos(0): Simplify the expression using the fact that cos(0) = 1: (cos(0))/(cos(0))Final Simplification: Since cos(0) = 1, the expression simplifies to: 1/1Simplify Fraction: Simplify the fraction: 1/1 = 1

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( $54$ ) $\lim _{x \rightarrow 0} \frac{\cos (4 x)}{\cos (2 x)}$

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Algebra 2

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Q. (

54

)

\lim _{x \rightarrow 0} \frac{\cos (4 x)}{\cos (2 x)}

Given Limit Expression: We are given the limit expression: $\newline$ $\lim_{x \to 0}\left(\frac{\cos(4x)}{\cos(2x)}\right)$ $\newline$ To solve this limit, we will directly substitute the value of $x$ as $0$ , since $\cos(4x)$ and $\cos(2x)$ are continuous functions and there is no indeterminate form.
Substitute $x = 0$ : Substitute $x = 0$ into the expression: $\frac{\cos(4\cdot 0)}{\cos(2\cdot 0)}$
Simplify Using $\cos(0)$ : Simplify the expression using the fact that $\cos(0) = 1$ : $\frac{\cos(0)}{\cos(0)}$
Final Simplification: Since $\cos(0) = 1$ , the expression simplifies to: $\newline$ $\frac{1}{1}$
Simplify Fraction: Simplify the fraction: $\frac{1}{1} = 1$