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Vu cxg i. ¸ Ø Ò ³ V Ó · í n ¸ t ¾ ) t ¢ Ç ¨ ¸ V Ó % ¸ Û £ / Ò µ Ð ¢ Ô t ÿ ä ë 8 Í ý ó 3 · Ó · 2 ³ ¡ u ´ Ñ Ó Ï r Ó Ç ¢ u Í É Û ½ £ / !. Í v y z ~ ° ¶ · ¸ } w { x ¯ ´ ~ ¯ x z w ± } ° ³ ´ y Î Î { y ° ~} z ± w ¯ ³ x ´ x y z ° ~ ± {} ³ ¯ {x y ~ z} ­ p l g n f j b m h d Ï Ð v Ñ ® Ò Ó Ñ Ô ¶ Ò Õ Ö ~ x ¶} ° z × ³ Ø y Ù v Ú Ñ Ô ® Û Ð Ò Õ Ó Ü Ø ¶ Ï × Ò ® Ð Ù v Ó Ñ Ô Õ Ù x ~ z Ñ { ³ Ï ­ Ø ¸ Ý Ü x Ù z Þ. Y ³ ³ ³ f f and f ( y ) 0 otherwise 11 marginal pdf of Y marginal pdf of Y you check Notes 1 x cannot appear in (y can‟t be in ) 2 You must give the ranges;.

Jun 09, 11 · you cannot take this equation as a straightforward statement of how an economy works It is, after all, merely an identity It is true by definition but tells you nothing about the underlying dynamics inside an economy. ³ § ª§± ¨ ´ ± § ~§ ¨ ° ³Ã ½ v l§Ã ½ U ¢ w ª U c U § Y ´ S U ³ § ± U ¶ à Y ½ ´ º § ¿ U ¿ ¨ c À U w Y ÐÎÐÐ ý U » W ¦ U x § ¸ ¼ ¨ là ª U Y ¿ U ± § § Y ¹ µ » º § ½ ´ º § Y ¢Í Ê § Y. 7 # 2 ) &,) &'( &,).

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D,, / v µ v P v Ç t Z } } v } ( v v í X d Ç } } u } Ç } µ o ( ~ Ç o u v µ v } v Z Ì o P Z X. 5 6 0e5 0 *5 bc0 = 3 *d @ > ¦ @ ~ p§j ¦ yªw ³ §d ª° >ª / > /. This preview shows page 3 6 out of 9 pages \ D S k o G f d t ^ w p a k r _ e N _ L m L x C t a b R A n l b l U g r K i q g s h t b s _ j r _ e y s F e c r V v r e p d i B b q M b a _ d t e C f w Z i G t D h W j I g n d f c i B n r i t K e r n A l s g P e a b ` r n a I P 1 P Worksheet by Kuta Software LLC3Solve each inequality 21) 1 2 £ a 10 A) a £ 1 B) a ³ 5 C) a ³ 19 2.

³ Chain Rule Version d gx ³ a f t dt f g x g x dx c _____ Average value of f (x) on a, b 1 b AVE a f f x dx ba ³ Volume around a horizontal axis by discs ( )2 b a V r x dxS³ Volume around a horizontal axis by washers ( ( ) ( ) )22 b a V R x r x dx S³ Volume by cross sections taken perpendicular to the xaxis b a V A x dx ³. 5 Below are the graphs of x f x x 1 1 and the linear approximation f (x) 1 Notice, the line provides a good approximation of the function for values of x that are very close to x = 0 In Math 111, we learned a formula for the linear approximation of a function near a point x = a Using our function and x = 0, we use this formula and get the same linear approximation. W 16 N9 1 i ؁j000 `16 N9 28 i j2359 W e u C { E u b N X v V Y ̃ r i z A G s \ h j.

³ Ç Þ É Æ Í Ò ¹ Á ° ­ È ß ´ É µ º ¸ Å Ä ² Í ­ È ± ¯ ¹ ³ Ã Ç Â ¶ Ñ Á ° Ü Ý Æ à ­ Ø á º ¸ ³ ´ Ò â ¯ Â Í ¬ Ú ã Ê ± ¹ Å É ° Ä µ ² ä ¶ Ã Á Ç » Ï Ð Ø Ã ¯ ¸ Ä ³ ´ ± µ ¼ Å ­ ® ° ² ¶ · ¹ º Ý å æ ç è Ì Á Â Ò É Í Ç ä · ´ ² º ¸ ³ Ç é Å Ã µ Í. ME 270 – Fall 14 Exam 1 NAME (Last, First) _____ ME 270 Exam 1 – Fall 14 Page 10 c) Using your freebody diagram, determine the magnitudes of the reactions at support O that are necessary to hold the bar in static equilibrium (11pts) d) If the applied 150Nm couple at A were shifted toward point B, what effect would this have on the. M h Õ 8 ¼ g ¢ è 9 z å £ w A L z t s x F ¨ w c º p K z Ë Ò Å ¢ v « ² A y ÷ ³ y y y N ¢ Ë £ y ¢ À µ Ä ç Ù æ ¤ ½ è ï Ø Ä ç £ ² A Y ³ £ y Ô ý.

I c x dx³ o reduced to 1d integral Likewise 2 ³ x 1 2 2 2 2, ( ) , ( ) x dP I g x P x h x P x dx dx ªº «» ¬¼ o integrals are different But they are the same if and only df is an exact differential If df exact differential then I I x y I x y 1 ( , ) ( , ) final initial Exact vs Inexact Differential Inexact differential (. í^ð ML @í ñjº * ON °²¸. ¹ µ º b4 J Ç É4 Ð ¶ Ô º ³ ¼ ¶ ,1 Û l p Û / ¹ µ º b4 J N #(ê Ô º Á Û Ü § U \ c p Û / ¹ µ º b4 J ü ¹ µ º b4 J Ç5 H Ð ¶ À Ô Ô ¹ µ º b4 J Æ#ã 8Á ³ ² ¯ á ¾ ¿4 í 'g' Ü p Û / ¹ µ º b4 J ¹ µ º b4 J'.

V u G X p V i T f y C g ߉t E e 1L iJAN R h j ̃y W ł B i 11 `15 c Ɠ ȓ ɔ ܂ i y j j B DCM I C ̓T f y C g( ) ̂ ߉t E ܂ w z Z ^ ʔ̃T C g ł BDCM I C ł͓h E C p i ͂ ߂Ƃ A 34 _ ̏ i 舵. 2 i 7 ³ L L < Ç M t < M A k J A * N E i 6 K 2 º Ç E ³ L M m y  t A Ë E L n F Ê H º 2 ½ Q Ò J Î K M 2 @ T 2 L C m 2 º I Q m  6 2 m 6 ³ L T E m N A ³ L · L s G 6 7 x s É. ² { M Í w « ³ { M Í w « y 6 T Z ` h a ¼ x z í M s r w Ú ù Ô « ¢ µ ¢ £ w p h Ô t Z o b \ q { Q ¼ g y 7 4 A ÷ a ¼ ;.

Writing is not enough 4 Math convention writing with no range means it‟s right for all y, which is very wrong in this example. D Z µ Ç U D Z í U î ì í ô õ W ï î WD PDWK E Z 3DJH > µ î ð W h v µ v } ( o P o } µ d Z µ Ç U D Z í U î ì í ô õ W ð õ WD PDWK E Z 3DJH Title math0b18w. 0 U" X ^ ³ _ ± ± 3 x = 0Q` § a ³ x = h 0 i Q x = " 0 # ° a4 § ° b Q§ ^ n = 1 Q n = 2 x 0 1 0 A » ± D 2 4 6 1 3 Q 2 ´² Q 0 7 5 6 40 1 3 ²´ ¡§ 0 0 7 c 74 6 ³± ³.

C ¹ V ² ü ¼ ã É ¨ ¯ é ´ ê Ë Ý J L O Y µ Ä ~ º Ý õ ð g Ý § Ä ½ D ~ º É g p · é û ³ W b L O z C X g i è i0tf j ð8 î Ý u µ ½ D ¢ ¤ ¢ ï È ð É à Ö í ç ¸ g u È ­ C ³ É ® ¹ û X É ´ Ó v µ Ü · D. International trade has got an enormous impact in every country’s national income National economy that is not (or less) integrated in the international economy will stagnate on the supply side, which caused by the lack of market potential to absorb increased production (economic growth) in the country’s economic activities. Jun 28, 16 · Email;.

³ ³ ³ ³ ³ ³ ³³ EJEMPLO N° 1 Describir la primitiva de 7x Solución 11 2 2 7 7 Regla de multiplo constante =7 Reescribir (x = x ) x =7 C Regla de la po ntencias (n = 1) 2 7 = x Simplificar 2 xdx x dx x dx C ³³ ³ En este ejemplo se pueden apreciar tres pasos para encontrar la. Ç ¶ t ù d o Í É ç w M ü Z U D ó t s b { Í É ç ¨ U ¨ T ¬ b ³ æ ¶ ¬ ¶ 7 G Z X ¹ å Í É ç Z ³ æ ¶ ' ± ¶ Ü 451 4 8GIN. }$Î @ í B M ¿ å ³ ¤ å Ì É ³ » _ X 8 Z c H* _ ó ° K Z $ª w E Z 8 S T C S u Ì É ³.

Those who have taken economics courses may remember the equation above, which lists the components of GDP GDP (Y) is the combination of consumption (C), investment (I), government spending (G), and net exports (exports (X) less imports (M)). ¤ î ¨ ¿ £ > Ñ è À à Ë ³ 2 ñ ¤ î ¨ ¿ £ > Ñ è À à Ë ³ \ 7 ¤ ß x} Ô Ñ Ø > Þ ¿ ð > ä x} Ô a î ¨ à Ñ è ÿ \. æ t E æ µ v Ì ¨ è ¢ v µ Ü · B È ¨ { Í K ¸ ¨ q l É ¨ n µ ­ ¾ ³ ¢ B A h o C X Ó x ì Æ ð s ¤ O É K ¸ ¨ Ç Ý É È è A À S Å m À È æ t ¯ ì Æ ð s Á Ä ­ ¾ ³ ¢ B.

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¼M @ !œ öq ’TU Ms;–Ç ó(æóIW3 Þ½sïdµ d F¢‘h$ , ²BY'. F = w x dx³ eq ³L 0 xF = x w x dx Centroids x dA c x = dA ³ ³ c dA y = dA ³y ³ ci i i i i xA x = A ¦ ¦ ci i i i i yA y = A ¦ ¦ In 3D, ci i i i i xV x = V ¦ ¦ Centers of Mass x cm!G$ x = !G$ ³ ³ y cm!G$ y = !G$ ³ ³ cmi i i i ii i x !$ x = !$ ¦ ¦ cmi i i i ii i y !$ y = !$ ¦ ¦ Buoyancy F gV B U Fluid Statics p gh U F p Lw eq avg. ³ dy ³ dt y 002 1 ln y 002t ln A y e002t ln A y e002teln A Ae 002t When t 0, y 0 Therefore A y e002t (ii) 000 e002t 2 e002t ln2 002t 347 002 ln2 t 6 (a) f c 2x 6x 10x 1 f 2x 6 3c 10 3 1 f 3 2 2 3 3 5 3 3 12 108 y 108 3x y x 141 (b) (i) lim lim 2 2 3 3 0 0 o o.

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³ 1 2 2 2 3 C u u u du Finally, translating back e e C e dx x x ³ 3 2 15 1 15 Example 3 Evaluate a) ³ x dx x 3 5 2 b) ³ dx x x 2 3 5 a) This is not a basic integral, but the composition is less obvious Here, we can treat the denominator as the inside of the 1/x function Let u dx x3 5 Then du 3x2 Solving for dx, 3x2 du dx. `V` dghVX^hr \^cr, `dchfda^fibiä eadhrä, ^ Xd_h^ X cdXiä \^cr, YZ XaVZqmghXih Xåhd_ @ik D Xdh dZcV\Zq, X 1997 YdZi, å dhmha^Xd igaqnVa. 1®aÒ aÞ,´"³ d"³ ¼5$ ó é 9 s ¯xb aî 7 Ä"³ d"³ añ ) x5$ ¼ « ol$ peÃ8#"³ ¼ 4*6 È d ý 1v cs Ä £ ¾ $ j b'6 3"³ d"³4ÿk0 v Ä lz , dnÓ lg = com ,´ ¡ ý Ä Ëlt & _ 9 x ¦( £e & ¹>õ ¾e e¶,´e7a35 > È } j 0 ûf Ä x ¹>õ 7f Õ ` f ¡ ý `e"d35 ,´lt & { } È"³.

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í 2A0è9 3û b0è ¢ Þ î » 2A b Ì É ³ » c 0 4 b4#&ì ç I 0è '¼ b g$ _ X 8 Z b0è9 @/ Z > ~ r O S T K \%Ê'2 ?. ° V Ó Û í n ¢ Ô & ó ¸ t ³ ß " Í Ï r ´ Ö ¡ ¨ 1 m æ ù ³ ² · W 0. ³ >Y m = 3 r ¡§ ° m = 3 = n = 1 r = n = 2x;Z³§ N(A) = f0g > » Ax = 2 0 1 3 1 ¨ Q± » Q§x \U 8 ³ ¦ » § » 3 Q±³» 6 ³ Q§V 4 8 0 5 7 Ax = 0;.