Question

Evaluate the limit limₓ→ 2π 4(π−2x)tan(x).

A) 0
B) [infinity]
C) −[infinity]
D) The limit is undefined.
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Answer 1

To evaluate the limit limₓ→ 2π 4(π−2x)tan(x), substitute 2π for x, simplify the expression, and evaluate the tangent function. The limit is 0.

Step-by-step explanation:

To evaluate the limit limₓ→ 2π 4(π−2x)tan(x), we substitute 2π for x in the expression:

4(π−2x)tan(x)

By plugging in x = 2π, we get:

4(π−2(2π))tan(2π)

Simplifying, we have:

4(π−4π)tan(2π)

And further simplifying:

4(-3π)tan(2π)

Finally, we evaluate the tangent function at 2π, which is 0:

4(-3π)(0)

Since anything multiplied by 0 is 0, the limit limₓ→ 2π 4(π−2x)tan(x) equals 0. Therefore, the answer is A) 0.