V63_0121_020_2008F_1c-sol

V63_0121_020_2008F_1c-sol - x 2 4 x-2 x x = lim x โ†’โˆž...

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Solution to V63.0121.020, Fall 2008 Midterm, Problem 1(c) October 13, 2009 We are asked to find lim x →∞ x 2 + 4 x - 2 x x . We can do this more than one way: (a) Dividing the fraction into a sum of two fractions: lim x →∞ x 2 + 4 x - 2 x x = lim x →∞ x 2 + 4 x x - 2 x x ! = lim x →∞ x 2 + 4 x x - 2 = lim x →∞ p 1 + 4 /x - 2 = - 1 (b) We can multiply by the conjugate radical: lim x →∞
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Unformatted text preview: x 2 + 4 x-2 x x = lim x โ†’โˆž โˆš x 2 + 4 x-2 x x ยท โˆš x 2 + 4 x + 2 x โˆš x 2 + 4 x + 2 x = lim x โ†’โˆž ( x 2 + 4 x )-(2 x ) 2 โˆš x 2 + 4 x + 2 x = lim x โ†’โˆž-3 x โˆš x 2 + 4 x + 2 x = lim x โ†’โˆž-3 p 1 + 4 /x + 2 =-3 1 + 2 =-1 . This corrects a mistake on the handwritten solution. 1...
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