HP 40gs hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 302
Solution 3, Solution 4, Solution 5
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hp40g+.book Page 28 Friday, December 9, 2005 1:03 AM 16-28 Solution 3 The calculator is not needed here. Simply stating that -x- en increases for x ∈ [0,2] is sufficient to yield the inequality: -x- 2-- 1 ≤ en ≤ en Solution 4 Since g(x) is positive over [0, 2], through multiplication we get: -x- 2-- g(x) ≤ g(x)en ≤ g(x)en and then, integrating: 2-- I ≤ un ≤ enI Solution 5 2-- First find the limit of en when n → + ∞ . Note: pressing after you have selected the infinity sign from the character map places a "+" character in front of the infinity sign. Selecting the entire expression and pressing yields: 1 In effect, 2-- tends to 0 as n n tends to + ∞ , so 2-- en tends to e0 = 1 as n tends to + ∞ . As n tends to + ∞ , un is the portion between I and a quantity that tends to I . Hence, un converges, and its limit is I . We have therefore shown that: L = I = 4 - ln2 Step-by-Step Examples