Question

Let F be the equation y=e²ˣ, let G be the equation x=9, and let H be the equation y=1.

Find the area of the region enclosed by the graphs of these equations. Use symbolic notation and fractions where needed.

Answer 1

The area of the region enclosed by the graphs of the equations y=e²ˣ, x=9, and y=1 is 0.

Step-by-step explanation:

To find the area of the region enclosed by the graphs of the equations y=e²ˣ, x=9, and y=1, we need to find the intersection points of these equations. Solving the equations, we find that the intersection points are (9, e²⁹) and (9, 1). The area of the region enclosed by the graphs is the area of the rectangle formed by these two intersection points.

The length of the rectangle is the difference between the y-coordinates of the intersection points, which is e²⁹ - 1. The width of the rectangle is the difference between the x-coordinates of the intersection points, which is 0. The formula to calculate the area of a rectangle is length x width, so the area of the region enclosed by the graphs is (e²⁹ - 1) x 0 = 0.

Therefore, the area of the region enclosed by the graphs of the equations y=e²ˣ, x=9, and y=1 is 0.