Question

The functions f and g are given by f(x)=√x and g(x)=6-x. Let R be the region bounded by the x-axis and the graphs of f and g, as shown in the figure in the link below. Please show your work.

h t t p://goo.gl/jXIZD

Answer 1

The functions f and g are given by f(x)=√x and g(x)=6-x. Let R be the region bounded by the x-axis and the graphs of f and g, as shown in the figure in the link below. Please show your work.

h t t p://goo.gl/jXIZD

1. Find the area of R.
2. The region R is the base of a solid. For each y, where 0<=y<=2, the cross section of the solid taken perpendicular to the y-axis is a rectangle whose base lies in R and whose height is 2y. Write, but do not evaluate, an integral expression that gives the volume of the solid.
3. There is a point P on the graph of f at which the line tangent to the graph of f is perpendicular to the graph of g. Find the coordinates of point P.

Answer 2

Can you upload a picture, because I can't open the link

Answer 3

Well, I will upload a picture

Answer 4

Painted area you need to find.

Answer 5

Firstly, you need to find x values, where these two graphis intersects. Do you know how to do it?

Answer 6

@Bladerunner1122

Answer 7

http://www.freeimagehosting.net/wzxvs

Answer 8

No, how do I do that?

Answer 9

And if possible it should be without the calculator.

Answer 10

Well, actually, you don't need to, because you have a pont (4;2) given. If you don't have any point, you need to solve this:
√x=6-x

Answer 11

Well, it is easy, you won't need to use a caculator

Answer 12

Secondly, you need to find there g(x)=6-x intersects Ox line, do you know why you need to do it?

Answer 13

Wouldn't g(x)=6-6?

Answer 14

Since I have the point I don't need to solve for it right?

Answer 15

no, g(x) intererects Ox when 0=6-x x=6