Larson: Chapter 1 problems

Here is a selection of problems from the first chapter of Larson's "Problem-solving through problems", 1983 edition:

• Read the comments at the beginning of each section - they describe the method.
  
  
• Section 1.1, Search for a patern: 1.1.1, 1.1.2, 1.1.5, 1.1.6 (write enough terms!), 1.1.9 (i.e., count mod 2), 1.1.11
  
  
• Section 1.2, Draw a figure: 1.2.3; 1.2.6 - 1.2.9
  
  
• Section 1.3, Formulate an equivalent problem: 1.3.2, 1.3.4; 1.3.8, 1.3.11
  
  
• Section 1.4, Modify the problem: 1.4.1, 1.4.4 (you probably saw this in Calculus III)
  
  
• Section 1.5, Choose effective notation: 1.5.1 (this is in the Math 2431 textbook), 1.5.3, 1.5.4; 1.5.7, 1.5.9
  
  
• Section 1.6, Exploit symmetry: comments before and after 1.6.1, 1.6.2, 1.6.4 (fill in the details); 1.6.8
  
  
• Section 1.7, Divide into cases: 1.7.2, 1.7.3; 1.7.5 (no need to look at "cases" if you use the correct approach!), 1.7.7, 1.7.8 (Hint: play with 0, 1, x.)
  
  
• Section 1.8, Work backward: the introductory example, 1.8.1,
  
  1.8.2 (although it does not matter for this problem, note that three numbers a, b, c are the sides of a triangle if and only if a=x+y, b=y+z, c=x+z with x, y, z > 0; one proof is to look at the inscribed circle)
  
  1.8.4; 1.8.5 (Typo: in part (b) replace the 2 in the LHS by 1.), 1.8.8
  
  
• Section 1.9, Argue by contradiction: introductory remarks, 1.9.2; 1.9.2, 1.9.3
  
  
• Section 1.10, Pursue parity: 1.10.1, 1.10.2; 1.10.6, 1.10.7, 1.10.8, 1.10.10
  
  
• Section 1.11, Consider extreme cases: 1.11.1, 1.11.2, 1.11.4; 1.11.6. 1.11.8
  
  
• Section 1.12, Generalize: 1.12.1, 1.12.2, 1.12.3; 1.12.5, 1.12.7