What is the equation of the line normal to # f(x)=x^2x2 # at # x=2#?
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The equation of the line normal to f(x)=x^2x2 at x=2 is y = 3x + 8.
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To find the equation of the line normal to (f(x) = x^2  x  2) at (x = 2), first, find the derivative of (f(x)). Then, find the slope of the tangent line at (x = 2). Since the line normal to the curve is perpendicular to the tangent line, its slope is the negative reciprocal of the slope of the tangent line. Finally, use the pointslope form to find the equation of the line.

Find (f'(x)): [f'(x) = 2x  1]

Evaluate (f'(2)) to find the slope of the tangent line at (x = 2): [f'(2) = 2(2)  1 = 3]

The slope of the line normal to the curve at (x = 2) is the negative reciprocal of the slope of the tangent line: [m_{\text{normal}} = \frac{1}{3}]

Now, use the pointslope form with the point ((2, f(2))) and the slope (m_{\text{normal}}): [y  f(2) = m_{\text{normal}}(x  2)]

Evaluate (f(2)): [f(2) = (2)^2  2(2)  2 = 2]

Substitute the values into the pointslope form: [y  2 = \frac{1}{3}(x  2)]

Simplify the equation to find the final answer: [y  2 = \frac{1}{3}x + \frac{2}{3}] [y = \frac{1}{3}x + \frac{8}{3}]
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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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