# How do you find the length of the curve #y=3x-2, 0<=x<=4#?

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The length of the curve ( y = 3x - 2 ) on the interval ([0, 4]) is given by the formula:

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

In this case, ( \frac{dy}{dx} = 3 ), so the integral becomes:

[ L = \int_{0}^{4} \sqrt{1 + 3^2} , dx ]

[ L = \int_{0}^{4} \sqrt{10} , dx ]

[ L = \sqrt{10} \int_{0}^{4} dx ]

[ L = \sqrt{10} \cdot \left[x\right]_{0}^{4} ]

[ L = \sqrt{10} \cdot (4 - 0) ]

[ L = \sqrt{10} \cdot 4 ]

[ L = 4\sqrt{10} ]

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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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