Hints for Homework Problems from Chapter 1

Section 1.2
        (2) See the examples on page 13.
        (3), (4) See the bottom of page 13 and the top of page 14.
        (5) See the bottom of page 14.
        (7) See Example 1.2.2.
        (8) See the bottom of page 18.
        (10) See the graphs of Example 1.2.3 in Figure 10.
        (11) See the bottom of page 19 and the graphs in Figures 12 and 13.
Section 1.3
         (1) See Example 1.3.1.
         (2b), (2c) See Example 1.3.2.
         (4b), (4e) See Example 1.3.3.
         (5), (6a), (6e) See Example 1.3.4.
         (7a), (7c), (7e) See Example 1.3.5.
Section 1.4
         (1), (2) See the top of page 35.
         (3a), (3b) See the middle of page 35.
         (4a), (4f), (4h) See Examples 1.4.1.
         (5c) See page 38.
         (7a), (7e), (7f) See pages 40, 41.
         (12), (13), (14b) See Example 1.4.3.
Section 1.5
         (1)
Use an intuitive understanding of limits.
         (2a) See Example 1.5.1 (1).
         (2b), (2d) See Example 1.5.7 (3).
         (2e) See Example 1.5.7 (10).
         (2f) Consider the graph of the function.
         (2h) See Example 1.5.1 (4a).
         (2i) See Example 1.5.7 (7).
         (2j) See Example 1.5.7 (10).
         (3b), (3c) See Example 1.5.5 (1).
         (3d) See Example 1.5.5 (2).
         (3g), (3i) See Example 1.5.7 (4).
         (3k) See Example 1.5.7 (8).
         (5a), (5b) See Example 1.5.7 (1), (2).
         (5d) See Example 1.5.7 (8).
         (5e) See Example 1.5.7 (7).
         (6b) See Example 1.5.8 (1).
         (6c) Apply a trigonometric identity to rewrite the numerator.
         (6f) First simplify this fraction as a function of cos theta and sin theta.
         (6h) First divide the numerator and denominator by sin theta.
         (6k) See Example 1.5.8 (2).
Section 1.6
         (1)
See Examples 1.6.1 and 1.6.2.
         (2a), (2b), (2e) See Examples 1.6.2.
         (3a), (3d) See Examples 1.6.3.
         (4a), (4c) See Example 1.6.4 (1).
         (5) Apply the Intermediate Value Theorem.
         (6a), (6c) See Example 1.6.5 (3).
         (7a) See Example 1.6.5 (2).
         (8) See Examples 1.6.7.
         (9) See Examples 1.6.6.

Hints for Homework Problems from Chapter 2

Section 2.2
         (1a), (1d) See Examples 2.2.1.
         (2a), (2d) See Examples 2.2.2 and 2.2.3.
         (3b), (3d) See Examples 2.2.4 (1) - (3).
         (4b), (4e) See Examples 2.2.4 (4), (5).
         (5b), (5d) See Examples 2.2.4 (6), (7).
         (7) Read Corollary 2.2.4 carefully. To justify an answer of "true" you must provide a proof while
              to justify an answer of "false" you must provide an example of failure.
        (8a), (8c) See Example 2.2.6 (2).
        (8f) See Example 2.2.5 (3). Also compute k'(0) by using the definition of the derivative.
        (9a), (9c), (9g) See Examples 2.2.6.
        (10a), (10c), (10e), (10f), (10h), (10i) See Examples 2.2.7.
Section 2.3
        (1a) See Examples 2.3.1.
        (1h), (1i) See Examples 2.3.3.
        (2b), (2e) See Examples 2.2.2, 2.3.1, 2.33.
        (3a), (3e) See Example 2.3.4, (2), (3).
        (4b), (4d), (4e) See Example 2.3.4 (1).
Section 2.4
        (1a)
See Examples 2.4.1.
        (1d), (1h) See Examples 2.4.1 and 2.4.4.
        (2a), (2d), (2f) See Example 2.4.3 (1)-(3).
        (3b) See Examples 2.2.2 and 2.4.3 (1)-(3).
        (4a), (4d) See Examples 2.4.3 (4), (5).
        (5a), (5b), (5e) See Examples 2.2.7 and 2.4.4.
        (6a), (6b) Use (2.4.1).
        (6d) Use (2.4.1) and implicit differentiation.
        (7a), (7b) Use (2.4.1).
        (8a), (8b) Use (2.4.4).
Section 2.5
        (1a), (1c), (1e), (1j) See Examples 2.5.1.
        (2a), (2b), (2c) See Examples 2.5.3.
        (3a), (3b), (3d), (3e) See Examples 2.4.3, 2.5.1 and 2.5.3.
        (4a), (4c) See Examples 2.2.2 and 2.5.1.
        (5) See Example 2.5.2 (2) and the proof of Proposition 2.5.2.
Section 2.6
        (1c), (1d) See Examples 2.6.1.
        (2a), (2b) See Examples 2.6.2.
        (3a), (3c) See Examples 2.6.3.
        (4), (5a), (5e) See Examples 2.6.4.
        (6a), (6c), (6f), (6j) See Examples 2.6.5.
        (7a), (7b), (7e), (7h), (7i), (7k) See Examples 2.6.8.
Section 2.7
        (1a), (1d)
See Examples 2.7.1.
        (2) See Examples 2.7.2.
        (3a), (3d) See Examples 2.7.3.
        (4a), (4c) See Examples 2.7.4.
        (5b), (5g), (5h) See Examples 2.7.2, 2.7.3 and 2.7.4.
        (6) See the discussion on page 195 of Figure 45.
        (7a), (7f), (7h), (7i) See Examples 2.7.5.
        (8a), (8g), (8h), (8v), (8x), (8y), (8aa) See Examples 2.7.6.
Section 2.8
        (1a), (1e)
See Example 2.8.1.
        (2), (6), (7), (12), (13) See Examples 2.8.2.
        (18), (19), (22), (23) See Examples 2.8.3.
Section 2.9
        (1)
See Examples 2.9.1.
        (8) See Examples 2.9.2.
        (11a), (11b), (11d), (11h) See Examples 2.9.3.
        (12a), (12d), (13), (16), (18) See Examples 2.9.4.
Section 2.10
        (1a), (4), (12), (15), (16), (17), (20)
Reread the general procedure for solving these problems on page 228.
         Then see Examples 2.10.1.
Section 2.12
       (1a), (1b), (1e)
See Examples 2.12.1.
       (2a), (2e), (2h) See Examples 2.12.2.
       (4a), (6), (11), (12), (14) See Examples 2.12.3.

Hints for Homework Problems from Chapter 3

Section 3.2
       (1a)
See Example 3.2.1.
       (1e) See Example 3.2.2.
       (2a) See Example 3.2.3 (2).
       (2g) See Example 3.2.3 (1).
       (3a) See Example 3.2.4 (2).
       (3g) See Example 3.2.4 (1).
       (4a) See Example 3.2.5 (4).
       (4c) See the right diagram in Figure 14.
       (4g) See Example 3.2.5 (1) and the left diagram in Figure 13.
       (4k) See Example 3.2.5 (2).
       (4n) What is the geometric shape of this region?
       (4p) See Example 3.2.5 (2).
       (5a) This region is the union of a triangle and a trapezoid.  Recall that the area of a trapezoid is its height
              times half the sum of the lengths of its bases.
      (6a) You should not need to use calculus here!
      (6c) See Example 3.2.7 (1). The region is a trapezoid.
      (6d) See Example 3.2.7 (1). The region is the union of two trapezoids.
      (7a) See Example 3.2.7 (1). The region is a triangle.
      (7b) See Example 3.2.7 (1). The region is the union of two triangles.
Section 3.3
      (1a)
See Example 3.3.1.
      (2a) See Example 3.3.2 (1).
      (2e) See Example 3.3.2 (2).
      (3e) See Example 3.3.7 (2).
      (3f) What is the integral of 3/x^2?
      (3j) See Corollary 3.3.5(i).
      (4b) See Example 3.3.3 (1).
      (4g) See Corollary 3.3.5(f).
      (4i) Use the additive property of the definite to separately calculate the area for x<0 and for x>0.
      (5d) See Example 3.3.4 (2).
      (5f) See Example 3.3.4 (2). Multiply out the function before integrating.
      (6b) See Example 3.3.5 (1).
      (6f) See Example 3.3.5 (2).
      (6i) Note that cos x = sin x when tan x = 1.
      (7a) See Example 3.3.6 (1).
      (7d) Integrate with respect to y, noting x = sin y.
      (7e) Solve for x, and integrate with respect to y.
      (8e) See Corollary 3.3.5(i) and Examples 3.2.7.