---------------------------------------------------------------
                        Honors Calculus II (MAC 3473), Fall 95
                 
	Homework Policy:
	+++++++++++++++

	(1) You may work in pairs and submit one paper.
	(2) Write on one side of the page.
	(3) All work must be written in a proper and
            coherent fashion:
            * Explain what you are doing;
            * Write in sentences (see the class notes
              or the examples in the textbook for
              proper style);
            * Label all graphs, axes, curves, 
              relevant points etc clearly;
	    * Show all necessary working;
            * Don't approximate unless asked to.
	(4) There will be homework assigned each day. 
            Usually it will be collected and at least 
            one problem will be graded.

---------------------------------------------------------------

	Homework Assignment 1 (Due Monday, August 28)
	
	p.125 #8, p.125 #12, p.201 #18, p.272 #32,

	Find the smallest constant c such that

                      1/2
        log(x) <  c  x,    for all x > 1,
               =                     =
	and prove your result.
	
	
---------------------------------------------------------------


	Homework Assignment 2 (Due Tuesday, August 29)
                              1/2
	(1) Let f(x) = (1 + x)  . Find f'(x) and f'(0). Hence
            find constants a and b such that
                   1/2 .
            (1 + x)    =  a + b x,    for x small.
                                                   1/2
            Test your answer by computing (1.00123)  .                    
                               .
	    NOTE: The symbol " = " means "is approximately equal to".

	(2) Find an approximation to the definite integral

                                   1
                                   /      2
                                  |   (- x )
                                  |  e       dx
                                  |
                                 /
                                 0

	   by using a Riemann sum with n=5.


---------------------------------------------------------------

	Homework Assignment 3 (Due Wednesday, August 30)

	p.327 #16, 24,  p.335 #18, 22,  p.336 #48

---------------------------------------------------------------

	Homework Assignment 4 (Due Friday September 1)
	
	1. p.369, # 8
	
	2. p.370,  # 30
	
	3. p.370,  # 44
	
	4. Let  a,b,c,d be constants. Prove that the function
	
	                                        a x + b
	                                 f(x) = -------
	                                        c x + d
	
	
	is one-to-one iff  ad-bc is not zero.
	
	
---------------------------------------------------------------

	Homework Assignment 5 (Due Tuesday September 5)
	
	1. p.376, #4
	
	2. p.376, #6
	
	3. p.376, #12
	
	4. p.376, #20
	
	5. p.376, #22
	
---------------------------------------------------------------

	Homework Assignment 6 (Due Friday September 8)

	1.   p.384 #16

	2.   p.384 #18

	3.
	(a) Read p. 383 on Fractals and Fractal dimension and do #38 p. 385.

	OR
	                            
	(b) Prove that if 
	                                    x
	                                    /
	                                   |
	                       f(x)  =     |  f(t) dt
	                                   |
	                                  /
	                                  0
	    then f = 0.

---------------------------------------------------------------

	Homework Assignment 7 (Due Tuesday September 12)
	
	1.   p.399 #38
	
	2.   p.399 #40
	
	3.   p.399 #46
	
	4.   p.399 #57

---------------------------------------------------------------
	
	Homework Assignment 8 (Due Friday September 15)
	
	1.   p.409 #34
	
	2.   p.409 #47
	
	3.   Find f'(0) if                 /
	                                  | g(x)             
	                                  | ---    x not 0
	                          f(x) = <   x
	                                  |
	                                  |  0     x = 0
	                                  \
	
	and g(0) = g'(0) = 0 and g"(0) = 17. 
	Show your reasoning.
	
---------------------------------------------------------------

	Homework Assignment 9 (Due Wednesday September 20)
	
	1. # 3(v),(vii)   [p.378 of the handout]
	
	2. # 4(ix),(x)   [p.379 of the handout]
	
	3. Prove the following reduction formula:
                                                           /
                                                          |         1
                                               (2 n - 3)  |  --------------- dx
  /                                                       |    2     (n - 1)
 |      1                      x                         /   (x  + 1)
 |  --------- dx = ------------------------- + --------------------------------
 |    2     n                  2     (n - 1)                2 n - 2
/   (x  + 1)       (2 n - 2) (x  + 1)



---------------------------------------------------------------

	Homework Assignment 10 (Due Tuesday September 26)
	
	MAC 3312  EXAM I, Spring 95

---------------------------------------------------------------
	
	Homework Assignment 11 (Due Wednesday September 27)
	
	1. # 2 p.476
	
	2. # 8 p.476
	
---------------------------------------------------------------
	
	Homework Assignment 12 (Due Monday October 9)
	
	# 70, 72 and 74  p.487

---------------------------------------------------------------

	Homework Assignment 13 (Due Monday October 16)

	# 34, 38   p.500

---------------------------------------------------------------

	Homework Assignment 14 (Due Monday October 30)

	Do any 8 of the following problems.

	Questions 3, 4, 6, 7, 8 Spring Test 2 (see Old Exams).

	# 16, p.549
	
	# 26, p.561
	
	# 2, p.567
	
	# 22, p.567
	
	# 26, p.567

---------------------------------------------------------------

	Homework Assignment 15 (Due Wednesday November 8)

	Do at least one part of #38, p.568. 
        (extra credit for other parts).

---------------------------------------------------------------