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Консультация № 108320
06.11.2007, 21:24
0.00 руб.
0
1
1
Добрый вечер! помогите пожалуйста, надо вычислить предел, используя формулу тейлора
Lim=cos 3x – e в степени (-x) -x/ln(1+x)+ln(1-x)
(логарифмы находятся в знаменателе дроби)
заранее благодарна!!!
Lim=cos 3x – e в степени (-x) -x/ln(1+x)+ln(1-x)
(логарифмы находятся в знаменателе дроби)
заранее благодарна!!!
Обсуждение
Неизвестный
07.11.2007, 09:32
общий
это ответ
<font color=red><b>!!!</b></font>
Здравствуйте, Smilin!
Добрый вечер! помогите пожалуйста, надо вычислить предел, используя формулу тейлора
Lim=cos 3x – e в степени (-x) -x/ln(1+x)+ln(1-x)
(логарифмы находятся в знаменателе дроби)
заранее благодарна!!!
cos(3x) = 1 - (3x)^2/2 + o(x^2)
exp(-x) = 1 - x + x^2/2 + o(x^2)
cos(3x) - exp(-x) - x = -(3x)^2/2 - x^2/2 = -2x^2 + o(x^2) <font color=red>!!! -5x² + o(x²)</font>
ln(1+x) = x + x^2/2 + o(x^2) <font color=red>!!! x - x²/2 + o(x²)</font>
ln(1-x) = -x + x^2/2 + o(x^2) <font color=red>!!! -x - x²/2 + o(x²)</font>
ln(1+x)+ln(1-x) = x^2 + o(x^2) <font color=red>!!! -x² + o(x²)</font>
Lim [cos(3x) - exp(-x) - x]/[ln(1+x)+ln(1-x)] = Lim [-2x^2 + o(x^2)]/[x^2 + o(x^2)] = -2 <font color=red>!!! Правильный ответ: 5.</font>
<p><fieldset style=‘background-color:#EFEFEF; width:80%; border:red 1px solid; padding:10px;‘ class=fieldset><font color=red><i>Многочисленные ошибки</i>
-----
</font><font color=#777777 size=1><b>• Отредактировал: <a href=/info/user/118729 target=_blank>Агапов Марсель</a></b> (Специалист)
<b>• Дата редактирования:</b> 07.11.2007, 19:07</font></fieldset>
Здравствуйте, Smilin!
Добрый вечер! помогите пожалуйста, надо вычислить предел, используя формулу тейлора
Lim=cos 3x – e в степени (-x) -x/ln(1+x)+ln(1-x)
(логарифмы находятся в знаменателе дроби)
заранее благодарна!!!
cos(3x) = 1 - (3x)^2/2 + o(x^2)
exp(-x) = 1 - x + x^2/2 + o(x^2)
cos(3x) - exp(-x) - x = -(3x)^2/2 - x^2/2 = -2x^2 + o(x^2) <font color=red>!!! -5x² + o(x²)</font>
ln(1+x) = x + x^2/2 + o(x^2) <font color=red>!!! x - x²/2 + o(x²)</font>
ln(1-x) = -x + x^2/2 + o(x^2) <font color=red>!!! -x - x²/2 + o(x²)</font>
ln(1+x)+ln(1-x) = x^2 + o(x^2) <font color=red>!!! -x² + o(x²)</font>
Lim [cos(3x) - exp(-x) - x]/[ln(1+x)+ln(1-x)] = Lim [-2x^2 + o(x^2)]/[x^2 + o(x^2)] = -2 <font color=red>!!! Правильный ответ: 5.</font>
<p><fieldset style=‘background-color:#EFEFEF; width:80%; border:red 1px solid; padding:10px;‘ class=fieldset><font color=red><i>Многочисленные ошибки</i>
-----
</font><font color=#777777 size=1><b>• Отредактировал: <a href=/info/user/118729 target=_blank>Агапов Марсель</a></b> (Специалист)
<b>• Дата редактирования:</b> 07.11.2007, 19:07</font></fieldset>
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