# How do you find the arc length of the curve #y=(5sqrt7)/3x^(3/2)-9# over the interval [0,5]?

Here:

Then the arc length desired is:

Integrating using the power rule for integration:

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To find the arc length of the curve ( y = \frac{5\sqrt{7}}{3}x^{\frac{3}{2}} - 9 ) over the interval ([0,5]), follow these steps:

- Compute the derivative of ( y ) with respect to ( x ).
- Use the formula for arc length:

[ L = \int_{a}^{b} \sqrt{1 + \left(\frac{dy}{dx}\right)^2} , dx ]

- Plug in the derivative into the formula.
- Evaluate the integral over the given interval ([0,5]).

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To find the arc length of the curve y = (5√7)/3x^(3/2) - 9 over the interval [0, 5], we use the arc length formula:

Arc Length = ∫√[1 + (dy/dx)^2] dx

First, we find dy/dx by taking the derivative of y with respect to x.

Then, we plug this derivative into the formula and integrate over the given interval [0, 5].

Finally, we evaluate the integral to find the arc length.

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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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