How do you find the area between #g(x)=4/(2x), y=4, x=0#?
The area is
Therefore, the area is
graph{(y4/(2x))(y4)=0 [7.1, 6.95, 0.03, 6.99]}
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To find the area between the curves ( g(x) = \frac{4}{2  x} ), ( y = 4 ), and ( x = 0 ), you can follow these steps:
 Find the points of intersection between the curves ( g(x) ) and ( y = 4 ) by setting them equal to each other and solving for ( x ).
 Determine the interval over which ( g(x) ) is bounded by ( y = 4 ).
 Integrate ( g(x)  4 ) over the interval found in step 2 to calculate the area between the curves.
Let's go through these steps:

( g(x) = \frac{4}{2  x} ) intersects ( y = 4 ) when ( \frac{4}{2  x} = 4 ). Solving this equation gives ( x = 1 ).

The interval over which ( g(x) ) is bounded by ( y = 4 ) is from ( x = 0 ) to ( x = 1 ).

Integrate ( g(x)  4 ) from ( x = 0 ) to ( x = 1 ): [ \int_{0}^{1} \left( \frac{4}{2  x}  4 \right) dx ] [ = \int_{0}^{1} \left( \frac{4}{2  x}  \frac{4(2  x)}{2  x} \right) dx ] [ = \int_{0}^{1} \frac{4  4(2  x)}{2  x} dx ] [ = \int_{0}^{1} \frac{4  8 + 4x}{2  x} dx ] [ = \int_{0}^{1} \frac{4x  4}{2  x} dx ] [ = \int_{0}^{1} \frac{4(x  1)}{x  2} dx ]
You can then proceed to evaluate this integral to find the area between the curves.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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