Calculus 3 Practice Test 1

Show all work and justify each step.

(1) Show that the vector function

        
            
lies on the cone Sketch the curve.

(2) Determine all values of for which the vector function is continuous, where .

(3) Evaluate the definite integral



(4) Find given , , and

(5)  Describe and sketch the level curves for each of the following functions  
    (a) given

    (b) given

(6) State the domain for each of the following functions

    (a)      (b)  

(7) Find the value of the following limits, if they exist.

    (a)      
    
    (b)
    
    (c)

(8) Knowing that is a function of and , determine and   for each of the following:

     (a)       
     
     (b)
     
     (c)

(9) Find the equation of the tangent plane for each of the following surfaces at the given point.

    (a)   at the point
    
    (b) at the point

(10) Let Show that

(11) If show that

(12) Find the curvature for each of the following curves  

    (a) .
    
    (b) at .

(13) Find the total differential given

(14) Use differentials to approximate

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Cite this as:
Calculus 3 Practice Test 1
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/calculus-3-practice-test-1.html