Chapter102007 - Chapter 10 Test April 6, 2007 No...

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Unformatted text preview: Chapter 10 Test April 6, 2007 No Calculators Name y = - t + sin t where 0 £ t £ 2p 1. Find the point HsL at which the tangent to the curve is vertical if 1 x = ÄÄÄÄÄ t + cos t, 2 d2 y 2. Find ÄÄÄÄÄÄÄÄÄÄÄÄÄ Ä dx2 in terms of t if x = 12 t - t3 , y = t2 - 5 t 3. Find the length of the curve if x = t cos t - sin t, y = t sin t + cos t, and p 0 £ t £ ÄÄÄÄÄ 2 4. Evaluate the vector integral ii 3 ln t y i 2 yy jj Ä z j Ä zz ‡ jj ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ z i + j ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ z jz dt kk t { k t ln t { { e3 e 5. Find the unit vectors Hfour in allL that are tangent and normal to x = 2 t - t2 , y = 3 + t3 - t, at t=1 6. Find the slope of the tangent line for r = 1 + cos q, at 11 p Ä q = ÄÄÄÄÄÄÄÄÄÄÄÄÄ . 6 7. Sketch the graph of the polar equation, and be sure to label at least three polar points H r, q L, if r= "#### 3 + 2 sin q 8. Find the area of the region that is inside both r=2 and r2 = 8 sin 2 q 9. Find the area of the region that is inside r = 2 + 2 cos q and outside r = 6 cos q 10. Find the area of the region that is bounded by one loop of the polar equation r = 2 cos 3 q iqy jz 11. Find the length of the curve r = sin3 j ÄÄÄÄÄ z k3{ from q = 0 to q = 2 p 12. Replace the polar equation by an equivalent Cartesian equation. Then identify or describe the graph if r = 4 tan q sec q ...
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