Calc3 final 2017 copy.pdf - NAME Red Id MATH 252 Fall 2017...

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NAME: Red Id: MATH 252, Fall 2017 Final Examination version A I a ffi rm that I will not give or receive any unauthorized help on this exam, and that all work will be my own. Signature:
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1. Let P = (1 , 2 , 0) , Q = (2 , 1 , 0) and R = (3 , 2 , 0). a. Find , the angle between the two vectors u = QP and v = QR . (Note: is between 0 and .) b. Find | u v | . 2. Find the point(s) at which the line r 1 ( t ) = h 1 , 1 , 11 i + t h- 1 , 0 , - 2 i intersects the graph of the function z = f ( x, y ) = x 2 + y 2 . 2
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3. Set up (but do not evaluate) the integral to find the length of the curve r ( t ) = t i + t 2 j + t k over the interval 0 t 4. Simplify the integrand as much as possible. 4. Find the tangent line and the normal plane to the curve r ( t ) = h cos( t ) sin( t ) , cos 2 ( t ) , sin 2 ( t ) i at t = / 4. Equation of tangent line: Equation of normal plane: 3
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5. A particle travels along the parabola r ( t ) = h x ( t ) , y ( t ) i = h cos( t ) , sin 2 ( t ) i . How fast is its distance from the origin, f ( x, y ) = p x 2 + y 2 , changing at t = / 2.
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  • Fall '03
  • Bologna
  • Coordinate system, Polar coordinate system, Gradient

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