Nothing Special   »   [go: up one dir, main page]
Scribd Logo
Upload

Welcome to Scribd!

  • 21 views

    Faculty of Engineering (Chem., and Pet.) Semester One 2009 2010 Calculus MTHE01C02: Instructions Five Problems

    Uploaded by

    mostafa
    This calculus assignment from the Faculty of Engineering consists of 5 problems related to calculus concepts like limits, derivatives, gradients, directional derivatives, and finding extrema. Students are instructed to show their work and solutions after each problem on the provided paper or the back of the pages. The assignment is worth 10% of the total grade and is due on Sunday November 22nd. Good luck is wished to the student working on the problems.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd

    Faculty of Engineering (Chem., and Pet.) Semester One 2009 2010 Calculus MTHE01C02: Instructions Five Problems

    Uploaded by

    mostafa
    21 views6 pages
    This calculus assignment from the Faculty of Engineering consists of 5 problems related to calculus concepts like limits, derivatives, gradients, directional derivatives, and finding extrema. Students are instructed to show their work and solutions after each problem on the provided paper or the back of the pages. The assignment is worth 10% of the total grade and is due on Sunday November 22nd. Good luck is wished to the student working on the problems.

    Original Description:

    assignment of bue

    Original Title

    Assignment 1

    Copyright

    © © All Rights Reserved

    Available Formats

    PDF, TXT or read online from Scribd

    Did you find this document useful?

    Is this content inappropriate?

    This calculus assignment from the Faculty of Engineering consists of 5 problems related to calculus concepts like limits, derivatives, gradients, directional derivatives, and finding extrema. Students are instructed to show their work and solutions after each problem on the provided paper or the back of the pages. The assignment is worth 10% of the total grade and is due on Sunday November 22nd. Good luck is wished to the student working on the problems.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    21 views6 pages

    Faculty of Engineering (Chem., and Pet.) Semester One 2009 2010 Calculus MTHE01C02: Instructions Five Problems

    Uploaded by

    mostafa
    This calculus assignment from the Faculty of Engineering consists of 5 problems related to calculus concepts like limits, derivatives, gradients, directional derivatives, and finding extrema. Students are instructed to show their work and solutions after each problem on the provided paper or the back of the pages. The assignment is worth 10% of the total grade and is due on Sunday November 22nd. Good luck is wished to the student working on the problems.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 6

     

      Faculty of Engineering (Chem., and Pet.)
      Semester One 2009‐2010
      Calculus MTHE01C02
      Instructions:
    (1) This assignment consists of FIVE PROBLEMS. 

    (2) Please write your answer in the same paper after each problem. 

    (3) You can also use the back of the papers. 

    (4) The weight of this assignment is (10 % ) of the total marks. 

    (5) The due date of this assignment is SUNDAY 22/11. 

    GOOD LUCK 

    Name: 
    I.D: 
    Department: 
    Group: 
                                               Problem 1 (20 ) 
    x
    (a) Let f ( x, y ) = . 
    1 + 4 − x2 − y 2

    (i) Sketch the domain D of f. 

    (ii) Find f (2,0), f (−2,0), f (2, −1) if it is in the domain 

    xy 3
    (b) Show that  lim  does not exist. 
    ( x, y )→(0,0) x4 + y 4

     
                                            Problem 2 (20 ) 
    a) Describe  the  level  surface  of  f (x , y , z ) = x 2 + y 2 + z 2 for  the  given 
    values k =1, 2. 

    b) Find  an  equation  of  the  level  surface  of  f (x , y , z ) = x 2 + y 2 that 


    contains the point p(1,2,5) and sketch the equation.  

     
                                     Problem 3 (20 ) 
    The dimensions of a closed rectangular box are measured as 3 feet, 4 feet, 
    1
    and  5  feet,  with  a  possible  error  of  ±   feet  in  each  measurement.  Use 
    16
    differentials to approximate the maximum error in the calculated the value 
    of  

          (i) The surface area                                            (ii) the volume    

     
                                               Problem 4 (20 ) 
    (a) Let f ( x, y ) = x 2 y 3 . 

    (i) Find the gradient of f at the point p(1,3). 

    (ii) Use the gradient to find the directional derivative of f at p(1,3)in 
    the direction from p(1,3) to   Q(‐1,3). 

     
                                               Problem 5 (20 ) 
    1 2 1
    If f ( x, y ) = x3 − y 3 + x 2 − 6 x + 32 y + 4 ,  find  the  local  extrema  and 
    3 3 2
    saddle points of f. 

    You might also like