Math

QuestionFind limx0cos2x3\lim _{x \rightarrow 0} \frac{\cos 2 x}{3}. Choose from: A) 0 B) 13\frac{1}{3} C) 23\frac{2}{3} D) does not exist.

Studdy Solution

STEP 1

Assumptions1. We are asked to find the limit of the function \frac{\cosx}{3} as xx approaches 00. . We know that the limit of a function as xx approaches a certain value is the value that the function approaches as xx gets closer and closer to that value.
3. We also know that the cosine of 00 is 11.

STEP 2

We can directly substitute x=0x=0 into the function because the function is defined at x=0x=0.limx0cos2x\lim{x \rightarrow0} \frac{\cos2x}{}

STEP 3

Substitute x=0x=0 into the function.
cos2(0)3\frac{\cos2(0)}{3}

STEP 4

implify the expression inside the cosine function.
cos03\frac{\cos0}{3}

STEP 5

Substitute the value of cos0\cos0 which is 11.
13\frac{1}{3}So, the result of limx0cos2x3\lim{x \rightarrow0} \frac{\cos2x}{3} is 13\frac{1}{3}, which corresponds to option B.

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