# How do you find the area between #f(x)=2-1/2x# and #g(x)=2-sqrtx#?

The area is

Start by finding the intersection points.

The intersection points are hence

Now, we do a rudimentary sketch of the graphs on one grid (only if you don't have access to a graphing calculator, of course).

Our process here is to subtract the area of the lower graph (

We start by finding the area of the upper graph.

Now for the lower graph.

We now subtract the first area from the second:

Hence, the area of the region between

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To find the area between the curves ( f(x) = 2 - \frac{1}{2}x ) and ( g(x) = 2 - \sqrt{x} ), you need to compute the definite integral of ( f(x) - g(x) ) from the points where the curves intersect. First, find the intersection points by setting ( f(x) = g(x) ) and solving for ( x ). Then integrate ( f(x) - g(x) ) over the interval between those intersection points.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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