M125.F16.Review1.pdf - MATH 125 Review 1 In order to...

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MATH 125 : Review 1 In order to practice for Test 1, do as many problems as you can. Review Section of Chapter 1 in the book , do problems: # 15, 19, 21, 23, 25, 27, 29, 31, 33, 39, 45, 47. Problem 1 : Solve the following equations. a) 10 x = 5 x - 2 b) e x 2 - 8 x = 1 e 7 c) 2 ln ( x 3) - ln (3) = ln (3 - 2 x ) d) log 7 ( x + 1) = log 5 (2 x ) Problem 2 Evaluate the following limits if they exist. a) lim x →- 3 x 2 - 9 x 2 +2 x - 3 b)lim x 4 2 x 2 - 8 x | x - 4 | c)lim x 0 x ( sin ( π x 2 ) + 3) d)lim x 0 1 - 1 - x 2 x 2 e) lim x 0 cos (2 x ) - 1 sin ( x ) f) lim x 1 2 x 2 - 1 - 1 x - 1 g) lim x 0 sin ( x 2 ) sin ( x 3 ) h) lim x 0 xtan (5 x ) i) lim x 0+ 2 e 1 t e 1 t +1 j) lim x 1+ t 2 ln ( t - 1) Problem 3 Evaluate the following limits if they exist. a) lim x →∞ - 5 x 7 + 20 x 5 b) lim x →-∞ x 2 +3 x - 1 - 4 x +1 c) lim x →-∞ - x 2 +3 x - 1 7 x 2 - 5 x +30 d) lim x →∞ 3 x 4 +5 x 5 +1 1
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e) lim x →∞ 2 x +3 4 x - 10 f) lim x →∞ ln( x 3 +2 x - 4 2 x 3 +5 x +10 ) g) lim x →-∞ cos ( x ) - 1 x h) lim x →∞ x 2 + x 2 cos ( 1 x ) 3 x 2 - 2 x Problem 4
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