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HW8 - Math 191 7.6 10 a true b true 1 x 3 1 x HW 8...

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Math 191 HW 8 Solutions 7.6: 10 a. true; 1 x +3 1 x = x x +3 < 1 if x > 1 (or sufficiently large) b. true; 1 x + 1 x 2 1 x = 1 + 1 x < 2 if x > 1 (or sufficiently large) c. false; lim x →∞ 1 x - 1 x 2 1 x = lim x →∞ (1 - 1 x ) = 1 d. true; 2 + cos x 3 2+cos x 2 3 2 if x is sufficiently large e. true; e x + x e x = 1 + x e x and x e x 0 as x → ∞ ⇒ 1 + x e x < 2 if x is sufficiently large f. true; lim x →∞ x ln x x 2 = lim x →∞ ln x x = lim x →∞ 1 x 1 = 0 g. true; ln(ln x ) ln x < ln x ln x = 1 if x is sufficiently large h. false; lim x →∞ ln x ln( x 2 +1) = lim x →∞ 1 x 2 x x 2 +1 = lim x →∞ x 2 +1 2 x 2 = lim x →∞ ( 1 2 + 1 2 x 2 ) = 1 2 7.7: 4 a. π 6 b. - π 4 c. π 3 7.7: 6 a. 2 π 3 b. π 4 c. 5 π 6 7.7: 8 a. π 4 b. 5 π 6 c. π 3 7.7: 10 a. - π 4 b. π 3 c. - π 6 7.7: 14 α = tan - 1 ( 4 3 ) sin α = 4 5 , cos α = 3 5 , sec α = 5 3 , csc α 5 4 , and cot α = 3 4 7.7: 22 tan(sec - 1 1) + sin(csc - 1 ( - 2)) = tan(cos

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HW8 - Math 191 7.6 10 a true b true 1 x 3 1 x HW 8...

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