A circle's center is at #(7 ,2 )# and it passes through #(5 ,8 )#. What is the length of an arc covering #(7pi ) /4 # radians on the circle?
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To find the length of an arc covering ( \frac{7\pi}{4} ) radians on the circle, first, calculate the radius of the circle using the given center and a point it passes through, then use the formula for arc length.

Calculate the distance between the center of the circle ((7, 2)) and the point it passes through ( (5, 8) ) using the distance formula. [ \text{Distance} = \sqrt{(x_2  x_1)^2 + (y_2  y_1)^2} ]

Use the distance found as the radius of the circle.

Use the formula for arc length: [ \text{Arc Length} = \text{radius} \times \text{angle in radians} ]

Substitute the values to find the arc length.
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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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