Stitz-Zeager_College_Algebra_e-book

Example 1054 graph one cycle of the following

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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...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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