HP 40gs hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 300
or, simplifying
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hp40g+.book Page 26 Friday, December 9, 2005 1:03 AM Part 2 16-26 NOTE: The variable VX is now set to N. Reset it to X by pressing (to display CAS MODES screen) and change the INDEP VAR setting. To check the result, we can say that: lim e---x---------1-- = 1 x→0 x and that therefore: 2-- lim -e---n---------1- = 1 n → +∞ 2-- n or, simplifying: lim ⎛ ⎜ e 2-n - ⎞ 1⎟ ⋅n = 2 n → +∞⎝ ⎠ If the limit L of un exists as n approaches + ∞ in the inequalities in solution 2 above, we get: 3-- ⋅ 2 ≤ L ≤ 7-- ⋅ 2 2 4 1. Show that for every x in [0,2]: 2----x----+-----3x+2 = 2 - -----1-----x+2 2. Find the value of: ∫ I = 2 2----x----+-----3- dx 0 x+2 3. Show that for every x in [0,2]: -x- 2-- 1 ≤ en ≤ en 4. Deduce that: 2-- 1 ≤ un ≤ en ⋅ I 5. Show that un is convergent and find its limit, L. Step-by-Step Examples