What is the equation of the normal line of #f(x)= xsinx-cos^2x# at #x = pi/8#?
Apply product rule, chain rule and standard derivatives. The slope of The slope of a tangent ( The equation of a straight line of slope In this example, our normal will have the equation: We can see
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The equation of the normal line of f(x) = xsinx - cos^2x at x = pi/8 is y = -8x + 1.
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To find the equation of the normal line to ( f(x) = x \sin(x) - \cos^2(x) ) at ( x = \frac{\pi}{8} ), follow these steps:
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Calculate the derivative of ( f(x) ) to get the slope of the tangent line. [ f'(x) = \sin(x) + x \cos(x) + 2 \cos(x) \sin(x) ]
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Evaluate the derivative at ( x = \frac{\pi}{8} ): [ f'\left(\frac{\pi}{8}\right) = \sin\left(\frac{\pi}{8}\right) + \frac{\pi}{8} \cos\left(\frac{\pi}{8}\right) + 2 \cos\left(\frac{\pi}{8}\right) \sin\left(\frac{\pi}{8}\right) ]
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Calculate the slope of the tangent line at ( x = \frac{\pi}{8} ).
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The slope of the normal line is the negative reciprocal of the slope of the tangent line.
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Use the point-slope form of a line to write the equation of the normal line using the slope from step 4 and the point ( \left(\frac{\pi}{8}, f\left(\frac{\pi}{8}\right)\right) ).
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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.
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.
- What is the equation of the line tangent to #f(x)=x^2 + sin^2x # at #x=pi#?
- How do you find the equation of the line tangent to #f(x)=3/x^2# at x=2?
- How do you find the point on the graph of #y = x^2# where the tangent line is parallel to the line #x + 2y = 4#?
- How do you find the equation of the line tangent to #f(x)= 1/x#, at (1/2,2)?
- What is the equation of the tangent line of #f(x) =(2x-3)/(x-8)^2# at #x=3/2#?

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