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X ' 0 &!. D) f(x) = ln cos x e) f(x) = ln sen x f) f(x) = ln tg x g) 2 1 cosx f(x) sen x − = h) 1 senx 2 f(x) cosx = i) 2 senx f(x) 1 tg x = j) f(x) = 1 senx ln 1 senx − k) f(x) = 1 senx ln cosx l) f(x) = ( ) tg x2 ln cosx 2 73 Calcular la derivada de las siguientes funciones a) f(x) = arccos(x2) b) f(x) = arcsen ( 5x2) c) f(x) = arctg. þ!«Gü =#k È5 7 ê ,´ Ä Ä Â Ö Å 5 X F Â5 lF PAâ6f0S VN¶ ¸ J ê k È vFÓGü,´(é Z ê6h Ø G ê ëPÊ Õ µ 5 ¼?¯ ù V `,® FÓGü Ä O t j ¶ 5 ,´ ¹ ¡ È a 5 ¼?¯ ù ° · Ê ë È ` ¶FÓGü ÈF J 2 PAâ6f0S ÈAè J ê 5 Ce · £ k ¶ Ä v F Â5 lF ,´(é Z 5 °#§Eé ë È 6 5 V `Lõ ¨ Ä.
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F(n) = k=1 (k,n), donde (k,n) denota el maximo comu´n divisor de k y n (a) Probar que F(n) = X dn dϕ(n/d) (b) Dar una expresion de F(n) en t´erminos de la factorizaci´on can´onica de n 2 Demostrar que X n≤x √ n = 2x3/2 3 O(√ x) 3 Sea f0,∞) → 0,∞) una funcion nula para x < 2 (a) Demostrar que g(x) = X∞ n=1 1 n. I F 48,000 ~ @ r F00 r F0 u h N X ` E f B I Q l 艿155,400 ~ f ރf j W K h ~ J t J J L i S h j T C Y(cm)W42cmxH28cmxD13cm 55cm d lW d @ t @ X P2 Q l NNS R g 肨 Ȃ ݂̑ l C g b ^ n h o b O ł o b O S ̂ Dior ̃ S D 荞 ܂ꂽ W K h f ނŁA G ߊ 邱 Ƃ Ȃ N ʂ Ďg ͔ Q ł x g P b g ܂ Ńf j p c ̗l ȃf U C ł W i ׁ̈A ƃJ t ɏ X ܂ B C ɂȂ ł͂Ȃ A V i l Y Ȃ i. J 2 PAâ6f0S ÈAè J ê 5 Ce · £ k ¶ Ä v F Â5 lF ,´(é Z ê D E÷ È6h Ø 5 G ê Ä p È O t ï ` é È6< ¦ ÿ _ ê { pFP È ê º ¦ ÿ n X ê.
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