Final answer:
To find the area bounded by the graphs g(x)=2−x^4, y=4, x=0 and sketch the region, we need to find the points of intersection and their coordinates, and then plot the region between the graphs.
Step-by-step explanation:
To find the area bounded by the graphs g(x)=2−x4, y=4, x=0, we need to find the points where the graphs intersect. Let's set g(x) and y equal to each other: 2−x4 = 4. Solving this equation, we find x = ±√2.
These are the x-coordinates of the points where the graphs intersect. Next, we need to find the y-coordinate of the intersection point by substituting the x-coordinate into either g(x) or y.
Let's use y=4. So, at x = √2, y = 4. Similarly, at x = -√2, y = 4. Now we can sketch the region bounded by the graphs. It is a symmetric region between x = √2 and x = -√2, with y = 4 as the upper boundary and the x-axis as the lower boundary.