32sp10-fake-ex1-solutions

32sp10-fake-ex1-solutions - A GACCEEXA h e×eÔ ÖÓb ÐeÑ...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: A GACCEEXA# h e×eÔ ÖÓb ÐeÑ ×Û e Öe Ñ Ó ×Ø ÐÝ Øak eÒÓÓ fÓ Ðda ØheÜaÑ ×ÖeeØ iÒgØh eÑ a Øe Ö ia ÐØha ØÛ iÐÐ b eÓÚ e ÖedÓÒÓÙ ÖÖ×ØÑ id Øe ÖÑ eÜaÑ 665779885 C e ÖØa iÒ ÐÝ Øh e Öea Öea feÛ ØÓÓÑ aÒÝ Ô ÖÓb ÐeÑ ×h e ÖeØÓÓ ÖÖe×ÔÓÒd ØÓahÓÙ ÖeÜaÑ bÙ ØØh eÝg iÚ eÝÓÙ Øh e id eaÓ fØh e×Ó ÖØ×Ó fÔ ÖÓb ÐeÑ × Û h ihÑ igh Øb eÓÒ Øh eeÜaÑ F iÒd : a lim x →∞ parenleftBig 1 + r x parenrightBig x Ó ÐÙ Ø iÓÒ : iÒe ln parenleftBig lim x →∞ parenleftBig 1 + r x parenrightBig x parenrightBig = lim x →∞ ln parenleftBigparenleftBig 1 + r x parenrightBig x parenrightBig = lim x →∞ x parenleftBig ln parenleftBig 1 + r x parenrightBigparenrightBig = lim x →∞ ln ( 1 + r x ) 1 x = r lim x →∞ ln ( 1 + r x ) r x . ÓÛ ×e Ø h = r x ;aÒdÛ eÓÒ Ø iÒÙ eØh eabÓÚ eÛ iØh Øh eÓb ×e ÖÚa Ø iÓÒ Øha Ø ln(1) = 0 : = r lim h → ln (1 + h )- ln(1) h = r (ln( x )) ′ vextendsingle vextendsingle x =1 = r · 1 . b lim h → 4 h- 1 h Ó ÐÙ Ø iÓÒ : h i×i×b e×ØeÜÔ Ða iÒ ed iÒ Øe ÖÑ ×Ó fØh ed e Ö iÚa Ø iÚ eÓ feÜÔÓÒ eÒ Ø ia Ð× lim h → 4 h- 1 h = f ′ (0) , Û h e Öe f ( x ) = 4 x B Ù Ø× iÒe 4 x = e x ln(4) bÝ Øh eÖÙ Ðe×Ó fÐÓga Ö iØhÑ × lim h → 4 h- 1 h = f ′ (0) = d dx vextendsingle vextendsingle vextendsingle vextendsingle x =0 e x ln(4) = ln(4) ( e x ) ′ vextendsingle vextendsingle x =0 = ln(4) · 1 . d dx ( e − 2 x + 3 ln | x | ) vextendsingle vextendsingle vextendsingle vextendsingle x = − 1 / 2 Ó ÐÙ Ø iÓÒ : d dx ( e − 2 x + 3 ln | x | ) vextendsingle vextendsingle vextendsingle vextendsingle x = − 1 / 2 = parenleftbigg- 2 e − 2 x + 3 x parenrightbiggvextendsingle vextendsingle vextendsingle vextendsingle x = − 1 / 2 =- 2 e- 6 . A GACCEEXA# d d dx (arctan( x )) 2 vextendsingle vextendsingle vextendsingle vextendsingle x = − 1 Ó ÐÙ Ø iÓÒ : d dx (arctan( x )) 2 vextendsingle vextendsingle vextendsingle vextendsingle x = − 1 = 2(arctan( x )) 1 1 + x 2 vextendsingle vextendsingle vextendsingle vextendsingle x = − 1 = 1 . e sin(tan − 1 ( 1 2 )) Ó ÐÙ Ø iÓÒ : sin(tan − 1 ( 1 2 )) = sin( θ ) = 1 √ 5 , Û h e Öe tan( θ ) = 1 / 2 ×Ó sin( θ ) = 1 √ 5 . f tan(sin − 1 (1 / 3)) Ó ÐÙ Ø iÓÒ : tan(sin − 1 (1 / 3)) = tan( θ ) = 1 2 √ 2 , Û h e Öe sin( θ ) = 1 / 3 ×Ó tan( θ ) = 1 2 √ 2 g sinh(ln(2)) Ó ÐÙ Ø iÓÒ : sinh(ln(2)) = 1 2 ( e ln(2)- e − ln(2) ) = 1 2 (2- 1 2 ) = 3 4 . F iÒd Øh e iÒd ia Øed iÒ Øeg Öa Ð× :hÓÛ Øh e×ØeÔ × iÒÚÓ ÐÚ ed a integraldisplay x 2 sin x dx Ó ÐÙ Ø iÓÒ : a ÖØ× :ak e u = x 2 aÒd dv = sin( x ) dx h eÒ du = 2 xdx aÒd v =- cos( x ) dx integraldisplay x 2 sin x dx =- x 2 cos( x ) + integraldisplay 2 x cos( x ) dx, aÒdÒÓÛ dÓÔa ÖØ×aga iÒÛ iØh u = 2 x aÒd dv = cos( x ) dx ×Ó Øha Ø du = 2 dx aÒd v = sin( x ) h i×Û iÐÐÛ h iØØ ÐeaÛ aÝa...
View Full Document

{[ snackBarMessage ]}

Page1 / 12

32sp10-fake-ex1-solutions - A GACCEEXA h e×eÔ ÖÓb ÐeÑ...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online