Stitz-Zeager_College_Algebra_e-book

# Example 1054 graph one cycle of the following

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: eorem 9.2. In the same way the index k in the series ∞ ark−1 k=1 can never equal the upper limit ∞, but rather, ranges through all of the natural numbers, the index k in the union ∞ (2k + 1)π (2k + 3)π , 2 2 k=−∞ can never actually be ∞ or −∞, but rather, this conveys the idea that k ranges through all of the integers. Now that we have painstakingly determined the domain of F (t) = sec(t), it is time to 1 discuss the range. Once again, we appeal to the deﬁnition F (t) = sec(t) = cos(t) . The range of f (t) = cos(t) is [−1, 1], and since F (t) = sec(t) is undeﬁned when cos(t) = 0, we split our discussion into two cases: when 0 < cos(t) ≤ 1 and when −1 ≤ cos(t) < 0. If 0 < cos(t) ≤ 1, then we can 1 divide the inequality cos(t) ≤ 1 by cos(t) to obtain sec(t) = cos(t) ≥ 1. Moreover,using the notation 1 1 introduced in Section 4.2, we have that as cos(t) → 0+ , sec(t) = cos(t) ≈ very small (+) ≈ very big (+). In other words, as cos(t) → 0+ , sec(t) → ∞. If, on the other hand, if −1 ≤ cos(t) < 0, then divid...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern