# How do you find the volume of the solid formed when the area in the first quadrant bounded by the curves #y=e^x# and x = 3?

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To find the volume of the solid formed when the area in the first quadrant bounded by the curves ( y = e^x ) and ( x = 3 ), you can use the method of finding the volume of a solid of revolution.

Since the region is bounded by ( y = e^x ) and ( x = 3 ), you will be revolving this region about the x-axis.

The formula for finding the volume of a solid of revolution when revolving about the x-axis is:

[ V = \pi \int_{a}^{b} [f(x)]^2 , dx ]

In this case, ( a = 0 ) (the region starts from the y-axis) and ( b = 3 ) (the region ends at ( x = 3 )).

Thus, the volume ( V ) can be calculated as:

[ V = \pi \int_{0}^{3} [e^x]^2 , dx ]

Integrate ( [e^x]^2 ) from 0 to 3, and you'll get the volume of the solid formed by revolving the region about the x-axis.

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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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