# How do you sketch the region enclosed by #y=1+sqrtx, Y=(3+x)/3# and find the area?

Start by finding the intersection points of the two curves.

Integrate:

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To sketch the region enclosed by the curves ( y = 1 + \sqrt{x} ) and ( y = \frac{3 + x}{3} ), follow these steps:

- Graph the two functions on the same set of axes.
- Identify the points of intersection, which will determine the boundaries of the region.
- Determine which function is above the other between the points of intersection to establish the region's boundaries.
- Sketch the enclosed region.

To find the area of the enclosed region, integrate the upper curve's equation subtracted by the lower curve's equation within the interval where they intersect.

Here are the detailed steps:

- Graph the two functions ( y = 1 + \sqrt{x} ) and ( y = \frac{3 + x}{3} ) on the same set of axes.
- Identify the points of intersection by setting the equations equal to each other and solving for ( x ).
- Determine the interval where one function is above the other between the points of intersection.
- Sketch the enclosed region bounded by the two curves.
- Integrate the upper curve's equation minus the lower curve's equation within the interval of intersection to find the area of the enclosed region.

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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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