Where are the asymptotes of f(x) = tan (2x) from x = 0 to x = π?

Solution:

An asymptote is a line being approached by a curve but doesn't meet it infinitely.

In other words, you can say that asymptote is a line to which the curve converges.

The asymptote never crosses the curve even though they get infinitely close.

Given that:

f(x) = tan (2x) from x = 0 to x = π

f(x) = tan (2x)

It can be written as

f(x) = sin (2x)/ cos (2x)

We have to determine the value of x which makes cos (2x) = 0

cos (2x) = 0

2x = cos^-1 0

2x = π/2, 3π/2

x = π/4, 3π/4

cos (2x) has a period π.

The asymptotes of tan (2x) is when x = π/4 + nπ or 3π/4 + nπ from x = 0 to x = π

So the asymptotes of tan (2x) is when x = π/4, 3π/4

Therefore, the asymptotes are x = π/4, 3π/4.

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Where are the asymptotes of f(x) = tan (2x) from x = 0 to x = π?

Summary:

The asymptotes of f(x) = tan (2x) from x = 0 to x = π are x = π/4, 3π/4.