How do you find the equation of the perpendicular bisector of the points #(1,4)# and #(5,2)#?
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To find the equation of the perpendicular bisector of the line segment between the points ((1, 4)) and ((5, 2)):

Find the midpoint of the line segment using the midpoint formula: [ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) ]

Calculate the slope of the line passing through the two given points using the slope formula: [ m = \frac{{y_2  y_1}}{{x_2  x_1}} ]

Determine the negative reciprocal of the slope found in step 2 to obtain the slope of the perpendicular bisector.

Use the midpoint found in step 1 and the slope obtained in step 3 to write the equation of the perpendicular bisector using the pointslope form: [ y  y_1 = m_{\text{perpendicular}}(x  x_1) ]

Simplify the equation to obtain the final form.
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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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