Quiz 2 Question-Answer.version 2.pdf - MA105 Quiz 2 Date Div/Tut batch D/T CODE A Roll Number Name • Write the answer to each question in the space

Quiz 2 Question-Answer.version 2.pdf - MA105 Quiz 2 Date...

This preview shows page 1 - 2 out of 4 pages.

MA105 - Quiz 2 Date: 05/10/2018 Div/Tut batch: D / T CODE A Name: Roll Number: Write the answer to each question in the space provided below the question. You will be given supplements for rough work and they will not be collected. Write down your roll number on the supplements. Each question is of two marks. Failure to write the division, tutorial batch, name or roll number will result in a penalty of two marks each . Use of unfair means will result in heavy penalty. Calculators are not allowed. Mobile phones are not to be kept on person. If the final answer is a rational number then it should be given in its lowest form a/b where a, b are integers. If the expression for a or b is not simplified then you will not get any marks. Also answers can be written in decimals which have to be correct upto 2 decimal places. For example if the answer is 1 3 , then 0 . 33 or 0 . 333 is accepted but not 0 . 3 . Of course 0 . 4 is accepted for 0 . 40 . (1) Does the following function have a limit at (0 , 0) ? Give reasons for your answer. f ( x, y ) = x 2 y sin( x/y ) , if y 6 = 0 0 , if y = 0 . Answer: It does not. Then consider x n = 2 /nπ , y n = 4 /n 2 π 2 . Then f ( x n , y n ) = sin( nπ/ 2) , and lim n →∞ f ( x n , y n ) does not exist. This is a contradiction to the sequential criterion of limit. [Note: An answer with a wrong justification or no justification will carry no marks.] (2) Find the directional derivative D u f where f ( x, y ) = x 4 + 2 x 2 y 2 + 5 y 3 and u is the outward normal at the parabola y = x 2 at the point (1 , 1) . Answer: ± 1 5 (8 x 3 + 8 xy 2 - 4 x 2 y - 15 y 2 ) or 3 5 . (3) Find the maximum value of f ( x, y ) = x 2 y on the ellipse x 2 9 + y 2 4 = 1 . Answer: 4 3 . (4) Let D = { ( x, y ) R 2 : x 2 + y 2 a 2 } with a > 0 and f ( x, y ) = x 2 + y 2 for ( x, y ) D . Find the area of the smooth surface S given by z = f ( x, y ) on D .
Image of page 1

Subscribe to view the full document.

Image of page 2
  • Spring '16

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern

Ask Expert Tutors You can ask 0 bonus questions You can ask 0 questions (0 expire soon) You can ask 0 questions (will expire )
Answers in as fast as 15 minutes