Calculus I, Fall 2021 (Thomas’ Calculus Early Transcendentals 13ed), http://www.math.nthu.edu.tw/˜ wangwc/

Brief solutions to selected problems in homework week 15

1. Section 9.2, problems 4:

Figure 1: Section 9.2, problems 4.

Remark: One may assume that ln | cos x| = ln cos x. This amounts to finding the multiplication factor on the region cos x > 0. Since | cos x| = ± cos x, the effect of multiplying every term by \frac{1}{cos x} is the same as multiplying every term by \frac{−1}{cos x} and makes no difference in subsequent computations.

2. Section 7.3, problems 11, 37:

Figure 2: Section 7.3, problems 11, part 1. Figure 3: Section 7.3, problems 11, part 2.

Figure 4: Section 7.3, problems 11, part 3. Figure 5: Section 7.3, problems 37(a).

Figure 6: Section 7.3, problems 37(b).

3. Section 7.4, problems 10, 24:

Figure 7: Section 7.4, problems 10 (a,b).

Figure 8: Section 7.4, problems 10 (c,d). Figure 9: Section 7.4, problems 10 (e,f).

Figure 10: Section 7.4, problems 10 (g,h). Figure 11: Section 7.4, problems 24.