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2009a_x3b_sols

2009a_x3b_sols - Ó ÐÙ Ø iÓÒ ×ØÓE ÜaÑF Ó ÖÑB A...

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Unformatted text preview: Ó ÐÙ Ø iÓÒ ×ØÓE ÜaÑF Ó ÖÑB A B Ý Øh ed eÒ iØ iÓÒÓ fÐÓga Ö iØhÑ ifÙÒ Ø iÓÒ × x − 2 = 2 3 = 8 ×Ó x = 10 B h edÓÑ a iÒ i×a ÐÐ x ×Ùh Øha Ø − 1 ≤ x + 2 ≤ 1 Û h ihÑ eaÒ × − 3 ≤ x ≤ − 1 D h ed eÖ iÚa Ø iÚ e i× y ′ = 1 1 + x 2 − 1 ×Ó Øh e× ÐÓÔ e i× y ′ (1) = 1 1 + 1 2 − 1 = − 1 2 4 B ×e ÐÓga Ö iØhÑ id ieÖeÒ Ø ia Ø iÓÒ : ln y = ln( x sec x ) = sec x ln x y ′ y = sec x parenleftbigg 1 x parenrightbigg + sec x tan x ln x y ′ = x sec x parenleftBig sec x x + ln x sec x tan x parenrightBig 5 B A × x → + , ln x → −∞ aÒd x 2 → ×Ó Øh e ÐiÑ iØ i×e iØh eÖ ∞ Ó Ö −∞ . iÒeØh eÒÙÑ eÖa ØÓ Ö i×Ò ega Ø iÚ e aÔÔ ÖÓah iÒg −∞ aÒd Øh ed eÒÓÑ iÒa ØÓ Ö i×ÔÓ × iØ iÚ eØh e ÐiÑ iØ i× −∞ E Øha Ø × iÒeØh e ÐiÑ iØ i× iÒad e ØeÖÑ iÒ iØe fÓ ÖÑÛ e×hÓÙ ÐdÙ ×eÓ ×Ô iØa Ð×Ù Ðe 6 C h e ÐiÑ iØ i×Ó fØh e iÒd e ØeÖÑ iÒ iØe fÓ ÖÑ ×ÓÛ edÓÙ ×eÓ ×Ô iØa Ð×Ù ÐeØh i×Ø iÑ e : lim x → sin x + x cos x sin x . h i×i××Ø iÐÐÓ fØh e fÓ ÖÑ ×ÓÛ eaÒe iØh eÖÙ ×eÓ ×Ô iØa Ð×Ù Ðeaga iÒÓ Ö ÒÓ ØeØha ØØh eeÜÔ Öe×× iÓÒ × iÑ Ô Ðie×ØÓ lim x → 1 + x sin x (cos x ) = 1 + (1)(cos 0) = 1 + 1 = 2 7 D A ××ÙÑ iÒgeÜÔÓÒ eÒ Ø ia Ðg ÖÓÛ Øh Øh eeÕÙa Ø iÓÒ i× y = Ce kt ....
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2009a_x3b_sols - Ó ÐÙ Ø iÓÒ ×ØÓE ÜaÑF Ó ÖÑB A...

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