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Material Type: Exam; Class: Multivariate Calc; Subject: Mathematics; University: The University of Tennessee-Martin; Term: Fall 2005;
Typology: Exams
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Math 320 (Fall 2005) Second Test ______________________ Calculus III name (8 points)
This pleasant 50 minute test covers sections 12.7, 13.1-4, 14.1-2 of Calculus by Stewart 5th ed. Relax and do well. Unless otherwise stated, problems are 4 points.
⌠
π
cos t i + (1+ t^2 ) k dt
a) ρ cos φ = ρ sin φ cos θ in rectangular coordinates
b) ( x^2 + y^2 )^3 = xy in cylindrical coordinates
velocity v ( t )
speed v(t)
acceleration a ( t )
unit tangent vector T ( t )
the derivative T’ ( t )
unit normal vector N (0) (note t = 0)
binormal vector B (0)
e x
(^2) + y (^2) − 4
z x^2 + y^2 − 9
a.
lim ( x,y )→(0,0)
xy x^2 + y^2
b.
lim ( x,y,z )→(1,−1,1)
xyz x + y + z