Midterm Exam with Answer Key - Calculus and Analytic Geometry I | MATH 2433, Exams of Analytical Geometry and Calculus

Download Midterm Exam with Answer Key - Calculus and Analytic Geometry I | MATH 2433 and more Exams Analytical Geometry and Calculus in PDF only on Docsity! EXAM 1 Name Math 2433 2-25-11 Instructions Work all of the following problems in the space provided. If there is not enough room, you may write on the back sides of the pages. Give thorough explanations to receive full credit. 1. (24 points) A curve is given parametrically by the equations 2 = t+ é,y=Pie. Ayo 2tte® ee Ibe et cue & [+e%, 50 Ae Za Al “Thee @ O ©. © tl Find d?y/da?. (cee Scone") (26+8Je “/ ee Find "lt fe = £(3)> BG). alee) -L cer ® & Cres) Cres) © © if c. What is the slope of the curve at the point where t = 0? Explain your answer. - . © J 4% 44 ~ 2Ote* - Orla J ® Ax \y=5 I+ ee it 2 © (2 fE d. Is the curve concave up or down at the point where t = 0? Explain your answel2) ds > (Clee sOre)-or ede] _ lied @r)-ordel - £ hn re , ~ eee (e738 C03 2. (20 points)-The curve in the diagram is given parametrically by the equati 57 = the area of the region R enclosed by the curve in the first quadrant. page 2 Name 3. (12 points} Find the length of the portion of the polar curve r = 5cos@ that ties between the points A and B (see diagram). dt = -~Syn Ge 7 Se ) @ L L={* r+ fig) &0 © Om ° x - f Maio + UaK0 dO 9 ~ Kye Jaros 40 = | Ss0 oO = (re). |S |. @ 4. (24 points) Shown below is part of the polar curve r = a. a. Find the slope of the tangent to the curve at the point P (where 6 = 1. (12) ye HAO = Came &) x= ewe 2 ewO © _ fee +E we ga = do > JASE TY ax . - © 49 es [40 © & . dy ee eT OT ~ OKC At O-w, Te? Aw - Centr Eij-To . b. Find the area of the shaded region. { ) © 1 @ Az2{ do = oO 8 “(2 |" _ 30? 6 oC @ 7) NE Le 7 a CS 5 a, DB \y