114Final-F11

# 114Final-F11 - Final Exam Math 114 Fall 2011 Each problem...

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Unformatted text preview: Final Exam - Math 114 - Fall 2011 Each problem is worth 10 points. Circle your answers. In order to get full credit, you must both show your work and get the right answer. Name: (please print) Circle the name of your lecturer: Cooper Haglund Pantev Powers TA’s Name: (please print) Day of week and time of recitation: My signature below certifies that I have complied with the University of Pennsylvania’s Code of Academic Integrity in completing this examination Signature The table below is for grading purposes - do not write below this line 1 . 8 . 2 . 9 . 3 . 10 . 4 . 11 . 5 . 12 . 6 . 13 . 7 . 14 . 1 1. Find the area of the parallelogram three of whose vertices are (0 , , 0), (1 , 2 , 3), and (- 1 , 1 ,- 1). (A) √ 29 (B) √ 38 (C) √ 30 (D) 8 (E) √ 5 (F) 2 √ 5 (G) 6 2. Find r ( t ) if d 2 r dt 2 = h- t 2 , 1 ,- t i d r dt (1) = h 2 / 3 , ,- 1 / 2 i r (0) = h 1 ,- 1 , i What is the value of r (1)? (A) h 23 / 12 ,- 3 / 2 ,- 1 / 6 i (B) h 2 ,- 1 , i (C) h 2 , 1 , i (D) h 2- 1 , 1 i (E) h 2 , ,- 1 i (F) h 3 , , i (G) h 3 ,- 1 ,- 1 i 3. A spring gun at ground level fires a golf ball at an angle of 45 degrees. The ball lands ten meters away. Assuming the acceleration due to gravity is 9 . 8 m/s 2 , what is the balls initial speed? (A) 4 m/s (B) 5 . 2 m/s (C) 5 m/s (D) 5 √ 2 m/s (E) 10 m/s (F) 7 . 2 m/s (G) √ 98 m/s 4. Let L be the line through the origin that is perpendicular to the plane 2 x + y + z = 7. Find the distance between the point (- 4 , 3 , 5) and L . (A) √ 2 (B) (C) 1 / 5 (D) 5 √ 2 (E) 10 (F) √ 7 (G) 2 √ 15 5. Which of the following statements are true? (i) The curvature of the curve-→ r ( t ) = h 3 cos( t ) ,- 5 + 3 sin( t ) , 1 i is constant and equal to 1 / 2. (ii) If the acceleration of a motion-→ r ( t ) = h x ( t ) ,y ( t ) ,z ( t ) i is everywhere zero, then the trajectory of the motion is a circle. (A) (i) only (B) (ii) only (C) (i) and (ii) (D) none 6. Which of the following limits exist? (i) lim ( x,y ) → (0 , 0) x 4- y 4 x 2- y 2 (ii) lim ( x,y ) → (0 , 0) x- y x 2 + y 2 (iii) lim ( x,y ) → (0 , 0) x + y p x 2 + y 2 (A) (i) only (B) (ii) only (C) (iii) only (D) (i) and (ii) only (E) (i) and (iii) only (F) (ii) and (iii) only (G) none 7. Find the equation of the plane that is tangent to the surface cos( y + x )- sin( y + z ) = sin( z )- cos( x ) at the point ( π,π, 0). What is the y-coordinate of the point where this tangent plane inter- sects the y-axis? (A) 3 (B) π (C) (D) √ π (E) √ 3 (F) 1 (G) π/ √ 2 8. Find the product of the maximal and the minimal values of the function f ( x,y ) = x- 2 y + 2 xy in the region ( x- 1) 2 + ( y + 1 / 2) 2 ≤ 2 ....
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114Final-F11 - Final Exam Math 114 Fall 2011 Each problem...

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