Sketch the region enclosed by the given curves. Y = 2/x, y = 8x, y = 1/2 x, x > 0.
Solution:
Given equations Y = 2/x, y = 8x, y = 1/2 x, x > 0
Let us graph the linear equations by taking random values for x,y.
Draw the graph for the above three functions.
| x(x>0) | 1 | 2 | 3 | 4 |
| y=2/x | 2 | 1 | 2/3 | 1/2 |
| y=8x | 8 | 16 | 24 | 32 |
| y=x/2 | 1/2 | 1 | 3/2 | 2 |
The curve is y= 2/x
The straight blue line passing through the origin is the function of y = ½ x
The straight purple line passing through the origin is the function of y = 8x
The region enclosed between the three functions is shaded as shown above.
Sketch the region enclosed by the given curves. Y = 2/x, y = 8x, y = 1/2 x, x > 0.
Summary:
The sketch of the region enclosed by the given curves. Y = 2/x, y = 8x, y = 1/2 x, x > 0 is as shown above.