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Find the curvature of the curve r(t). r(t) = (10 + ln(sec \ t)) \ i + (8 + t) \ k, \frac...

Question:

Find the curvature of the curve r(t).

{eq}r(t) = (10 + ln(sec \ t)) \ i + (8 + t) \ k, \frac {-\Pi}{2} < t < \frac {\Pi}{2} \\r(t) = (3 + 9 \ cos \ 2t) \ i - (7 + 9 \ sin \ 2t) \ j + 2 \ k {/eq}

Curvature:

For {eq}r(t) {/eq},

{eq}\kappa (t)=\frac{\left \| r'(t)\times r''(t) \right \|}{\left \| r'(t) \right \|^3} {/eq}

Answer and Explanation:

{eq}r(t)=\left ( \ln (\sec t)+10,0,t+8 \right ) {/eq}

On differentiating with respect to t, we get

{eq}r'(t)=\left ( \tan t,0,1 \right ) {/eq}

On...

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from PSAT Prep: Tutoring Solution

Chapter 10 / Lesson 13
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