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Problem 24 Easy Difficulty

Use Formula 11 to find the curvature.
$$y=\tan x$$

Answer

$$\frac{|2\tan (x)\sec^2(x)|}{\left(1+\sec^4(x)\right)^{3/2}}$$

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Video Transcript

all right here. We want to find the curvature Kappa of the function. Why equals Tangent of X? So we know we're gonna need our first and second derivative. So let's go ahead and find those first derivative of Tangent of X is seeking Squared of X. And then the second derivative is a two times the tangent of X times See? Can't squared of X so we can go ahead and use the formula to find Kappa of X inter numerator We have the absolute value of the second derivative. So too tangent of X sequence squared of X And then in the denominator we have one plus the second place, the first derivative of why squared so that would be seeking it to the fourth power of X. And that entire quantity is give you raised to the three halfs power. And that is the curvature of why equals tangent of X

Campbell University
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