Question

Find the midpoints between the x-intercept and each of the vertical asymptotes of the function y = (5/2)tan(2x).

a) The midpoints cannot be determined without the specific function form.
b) The midpoints can be calculated with the given function.
c) The x-intercept and vertical asymptotes are unrelated.
d) Midpoints are irrelevant in the con of the function.

Answer 1

To find the midpoints between the x-intercept and each of the vertical asymptotes of the function y = (5/2)tan(2x), you need to determine the x-intercept and the vertical asymptotes.

Step-by-step explanation:

To find the midpoints between the x-intercept and each of the vertical asymptotes of the function y = (5/2)tan(2x), we need to first determine the x-intercept and the vertical asymptotes.

The x-intercept is found by setting y = 0 and solving for x. In this case, 0 = (5/2)tan(2x), so tan(2x) = 0. This occurs when 2x = nπ, where n is an integer. So, the x-intercept occurs at x = nπ/2.

The vertical asymptotes occur when the denominator of the tangent function, cos(2x), is equal to zero. This occurs when 2x = (n + 1/2)π, where n is an integer. So, the vertical asymptotes occur at x = (2n + 1/4)π/2.

Now, let's find the midpoints. Suppose we have an x-intercept at x = a and a vertical asymptote at x = b.

The midpoint between a and b is given by (a + b)/2. Applying this formula, the midpoint between x = nπ/2 and x = (2n + 1/4)π/2 is ((nπ/2) + ((2n + 1/4)π/2))/2.

Therefore, the midpoints between the x-intercept and each of the vertical asymptotes of the function y = (5/2)tan(2x) can be calculated with the given function.