Question

Find the slope of the tangent line to the curve in polar coordinates $r = 4\theta + 1$ at the value $\theta = \frac{\pi}{2}$. (Round your answer to three decimal places as necessary.)

          Find the slope of the tangent line to the curve in polar coordinates $r = 4\theta + 1$ at the value $\theta = \frac{\pi}{2}$.
(Round your answer to three decimal places as necessary.)
        
Find the slope of the tangent line to the curve in polar coordinates r = 4θ + 1 at the value θ = (π)/(2).
(Round your answer to three decimal places as necessary.)

Added by Samuel F.

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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Find the slope of the tangent line to the curve in polar coordinates T40+1 at the value 7T 2 (Round your answer to three decimal places as necessary.
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Transcript

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00:01 Hello students, in this question we have to find the slope of the tangent line to the polar curve.
00:06 Here the polar curve is given that r equal to 8 cos theta.
00:21 Here we have to find the slope so that we have to find dy by dx.
00:26 Here r equal to 8 cos theta is a circle so let us consider x equal to r cos theta and y equal to r sin theta.
00:35 Here we can replace r by 8 cos theta such that x equal to r cos theta which is written as 8 cos theta into cos theta such that we will get x equal to 8 cos square theta.
00:54 Then y equal to r sin theta.
00:57 Here we have to replace r by 8 cos theta into sin theta which is y.
01:06 So we need to find dx by d theta and dy by d theta.
01:13 So dx by d theta is 16 cos theta into minus sin theta.
01:29 So we can say that it is minus 16 cos theta sin theta which is dx by d theta.
01:36 Then we have to find dy by d theta which is equal to, so dy by d theta is minus sin square theta plus cos square theta...
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