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Length - Multivariate Calculus - Exam, Exams of Calculus

Dr. B.R. Ambedkar Open UniversityCalculus

This is the Exam of Multivariate Calculus and its key important points are: Length, Equation, Plane, Vector Equation, Perpendicular, Curve, Intersection, Parabola, Hyperbola, Ellipse

Typology: Exams

2012/2013

Uploaded on 02/14/2013

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arpanay ๐Ÿ‡ฎ๐Ÿ‡ณ

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MATH 261 โ€“ FALL 2000 โ€“ FIRST EXAM
September 26, 2000
STUDENT NAME โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”-
STUDENT ID โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”-
RECITATION HOUR โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”-
RECITATION INSTRUCTOR โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”
INSTRUCTIONS:
1. This test booklet has 5 pages including this one.
2. Fill in your name, your student ID number, your recitation hour
and your recitation instructorโ€™s name above.
3. There are 9 questions, each worth 11 points.
4. Questions 1 to 6 are multiple choice. Circle the letter of your choice
for the correct answer. No partial credit will be given.
5. Question 7 to 9 are partial credit. You should carefully explain your
solution. No points will be given to solutions without explanations.
6. No books, notes or calculators may be used.
โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€“ โ€”โ€”โ€”โ€“
1) Which of the following is an equation of the plane that contains the
point (โˆ’1,2,1) and is perpendicular to the line with vector equation
~r(t)=(โˆ’3+t)
~
i+(1โˆ’t)~
j+(4+2t)~
k.
A) xโˆ’y+z=โˆ’2
B) xโˆ’y+2z=โˆ’1
C) xโˆ’y+z=3
D) 2xโˆ’y+2z=โˆ’2
E) 2xโˆ’y+2z=1
1
pf3
pf4
pf5

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MATH 261 โ€“ FALL 2000 โ€“ FIRST EXAM

September 26, 2000 STUDENT NAME โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”- STUDENT ID โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”- RECITATION HOUR โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”- RECITATION INSTRUCTOR โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€” INSTRUCTIONS:

  1. This test booklet has 5 pages including this one.
  2. Fill in your name, your student ID number, your recitation hour and your recitation instructorโ€™s name above.
  3. There are 9 questions, each worth 11 points.4. Questions 1 to 6 are multiple choice. Circle the letter of your choice for the correct answer. No partial credit will be given.
  4. Question 7 to 9 are partial credit. You should carefully explain your solution. No points will be given to solutions without explanations.
  5. No books, notes or calculators may be used. โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€“ โ€”โ€”โ€”โ€“
  1. Which of the following is an equation of the plane that contains the point (โˆ’ 1 , 2 , 1) and is perpendicular to the line with vector equation ~r(t) = (โˆ’3 + t)~i + (1 โˆ’ t)~j + (4 + 2t)~k. A) x โˆ’ y + z = โˆ’ 2 B) x โˆ’ y + 2z = โˆ’ 1 C) x โˆ’ y + z = 3 D) 2x โˆ’ y + 2z = โˆ’ 2 E) 2x โˆ’ y + 2z = 1

1

  1. The length of the curve ~r(t) = t~i + t 22 ~j + (^23 โˆš 2 )^ t^32 ~k, for 0 โ‰ค t โ‰ค 2 is A) 1 B) (^43) C) 4 D) 23 โˆš 2 E) 2

  2. The intersection of the surface z = x^2 โˆ’y^2 +1 with the plane z = 2 is A) A line B) A circle C) An ellipse D) A parabola E) A hyperbola

  1. Which of the following are the symmetric equations for the line per- pendicular to the surface x^2 + y^2 + z^2 = 4 at (โˆš 2 , 1 , 1)? A) xโˆšโˆ’ 21 = y โˆ’ 1 = z โˆ’ 1. B) xโˆ’โˆšโˆš 2 2 = y โˆ’ 1 = z โˆ’ 1. C) x โˆ’ โˆš2 = y โˆ’ 1 = z โˆ’ 1 D) xโˆ’ 2 โˆš 2 = yโˆ’ 2 1 = yโˆ’ 21 E) x โˆ’ โˆš2 = y โˆ’ 1 = zโˆ’ 3 1.

Remark: Questions 7 to 9 require detailed solutions. No points will be given to answers without explanations. It is important to justify your steps. Even if you arrive at the correct answer, points will be deducted if your explanation is incorrect. 7)tion Find an equation of the plane tangent to the graph of the func- f (x, y) = sin(ฯ€xy) at the point ( 1 2 ,^13 ,^12 ).

  1. Does

(x,ylim)โ†’(0,0)^ x x^22 + 3^ + yy^22 exist? If so find its value.

  1. Find the position ~r(t) of an object with acceleration ~a(t) = ~k, initial velocity ~v 0 = ~i and initial position ~r 0 = ~j.