Use the diagram below to answer the question that...

Use the diagram below to answer the question that follows. The diagram shows the area of an overhead projection on a screen as a function of the distance, $x$, between the screen and the projector. Which of the following families of functions best models this situation? OA. $f(x) = mx + b$ OB. $f(x) = ax^2 + bx + c$ OC. $f(x) = \frac{k}{mx + c}$ OD. $f(x) = ab^x$

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00:01 We now determine the area enclosed by the two curves and the vertical lines.

00:05 The two curves are f of x equals e power x and g of x equals 1 over x.

00:11 And the two lines are x equal to 1 and x equal to 2.

00:15 So here i have drawn the sketch of the curves as well as the vertical lines.

00:21 So this one is the f of x equal to e power x.

00:25 So this is always an increasing function.

00:29 So the graph increases from left to right.

00:33 And then another curve, this is g of x equals 1 over x, which is a reciprocal function.

00:39 And it decreases above x -axis and it also decreases below the x -axis.

00:46 We will not consider this portion which lies below this x -axis.

00:51 This is also part of the g of x equals 1 over x function.

00:54 But we will consider only the portion of the curve which lies above the x -axis so that we get the enclosed region and we have the two lines x equal to one and x equal to two so as indicated in this diagram the region a b c d is the enclosed region and we have to determine the area of this region to determine its area we place this area between the curves formula which says that if you if we have two functions, f of x and g of x, defined in the interval a, comma, b, the area bounded by these two curves and the lines are given by integral of x equal to a and the upper limit is x equal to b.

01:42 The absolute value of f of x minus g of x, dx.

01:46 So let's use this formula to determine this enclosed region.

01:50 So i read down this area of region abcd...

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