2313Homework2

# 2313Homework2 - P 7 At what angle does the curve C...

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MAC 2313 Homework 2 YOU MUST SHOW YOUR WORK TO RECEIVE FULL CREDIT!! Supply answers below as indicated. Throughout the assignment, reference is made to the curve C deﬁned by the vector-valued function: -→ u ( t ) = < ln( t ) , 2 t , t 2 > for t > 0 1. Calculate and sketch the projections of the curve C in the three coordinate planes. 2. Write symmetric equations for the tangent line to curve C at the point P where it intersects the yz -plane. 3. Calculate the arclength function s ( t ) for curve C as t increases from point P . (Look for a perfect square root in your calculation.) What is the exact arclength from P to the point corresponding to t = e ?

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4. Calculate the curvature of curve C at the point P . 5. Calculate -→ T and -→ B , at the point P . Do not calculate -→ N to do this! 6. Write linear equations for the osculating and normal planes at point
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Unformatted text preview: P . 7. At what angle does the curve C intersect the yz-plane? That is, what angle does the tangent vector make with its projection in the yz-plane? 8. Calculate-→ N at the point P , from the vectors-→ T and-→ B . 9. Suppose that-→ u ( t ) represents the velocity of an object where t is time in seconds and the magnitude is measured in m/s. Find the displacement vector of the object from t = 1 to t = 4 . How far (round to 3 decimals) has the object traveled from its original position at t = 1 ? 10. Show that, more generally, the curve C has curvature κ ( t ) = 2 t (1 + 2 t 2 ) 2 . At what point does C have maximum curvature?...
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2313Homework2 - P 7 At what angle does the curve C...

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