# What is the arclength of #f(x)=e^(x^2-x) # in the interval #[0,15]#?

The general formula for Arc Length of a function of x is:

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To find the arc length of the function ( f(x) = e^{x^2 - x} ) on the interval ([0, 15]), we use the formula for arc length of a function ( f(x) ) on an interval ([a, b]):

[ L = \int_a^b \sqrt{1 + (f'(x))^2} , dx ]

First, we find the derivative of ( f(x) ) using the chain rule:

[ f'(x) = (2x - 1)e^{x^2 - x} ]

Then, we plug this derivative into the arc length formula:

[ L = \int_0^{15} \sqrt{1 + (2x - 1)^2e^{2(x^2 - x)}} , dx ]

This integral can be difficult to solve analytically. You may need to use numerical methods or software to approximate the value of the integral.

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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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