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Multiple Choice Problems and Partial Credit Problems.
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MATH 20550: Calculus III Practice Exam 1
Multiple Choice Problems
โ 11 2 (b)^
11 (c)
6 (d)
โ 6 2 (e) 1
(a) a (b) b (c) a โ b (d) |a|b (e) projba
(a) The line given by x = โt, y = 3 โ 3 t and z = โt. (b) The line given by x = โ 2 โ t, y = 1 โ 3 t and z = โt. (c) The line given by x = 1 + t, y = 6 โ t and z = 1 + 2t. (d) The plane 3x + 3y โ 3 z + 3 = 0. (e) The line given by x = 1 + t, y = 6 and z = 1 โ t.
r(t) = ใetโ^1 , t^2 , cos(1 โ t)ใ
when t = 1.
(a) x + 2y โ 3 = 0. (b) x + y + z โ 3 = 0. (c) x = 1 + t, y = 1 + 2t, z = 1. (d) Does not exist since rโฒ(0) = 0. (e) x + 2y โ 3 = 0 and z = 0.
5 is (a) (xโ4)^2 +(y +1)^2 +(z โ3)^2 = 5 (b) (xโ4)^2 +(y +1)^2 +(z โ3)^2 = 25 (c) (xโ4)^2 +(y+1)^2 +(zโ3)^2 =
5 (d) (x+4)^2 +(yโ1)^2 +(z+3)^2 = 5 (e) (x โ 4)^2 + (y โ 1)^2 + (z โ 3)^2 = 5
r(t) =< t^2 , โ 2 t, ln t >.
Find the tangential component aT and normal component aN of the ac- celeration at t = 1.
(a) aT = 1, aN = 2 (b) aT = 2, aN = 1 (c) aT = 1, aN = โ 2 (d) aT = 1, aN =
(e) aT =
5 , aN = 1
Find โ
(^2) f โxโy. (a) 5x^4 (b) (^) 1+^2 yy 2 (c) 20x^3 y (d) esin^ x^ cos x (e) esin^ x^ cos x + x^5 + (^) 1+^2 yy 2
Partial Credit Problems
r(t) =< โ ln t, t^2 , 2 t >, 1 โค t โค e.