ans-C-1-Ex1-F07

ans-C-1-Ex1-F07 - MATH 1431 EXAM 1 REVIEW I. LIMITS...

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MATH 1431 EXAM 1 REVIEW I. LIMITS “Algebraic expressions” 1. lim x →- 1 ± x 3 - 2 x 2 + 2 x 2 +8 ² = - 7 3 2. lim x 2 x 2 - 4 x +4 x 2 +2 x - 8 =0 3. lim x 2 x 3 - 8 x - 2 =12 4. lim x 2 + x - 2 x 2 - 4 Trigonometric expressions 5. lim x π/ 4 ³ sin 2 x · cos( x +3 π/ 4) ´ = - 1 2 6. lim x 0 3 x tan 2 x = 3 2 7. lim x 0 x 2 - 2 x sin 3 x = - 2 3 8. lim x 0 sin 2 2 x 4 x 2 =1 Piecewise defned Functions Set f ( x )= µ 2 x 2 ,x 0 2 - 2 x, x > 0 . 9. lim x 1 f ( x )=0 10. lim x →- 4 f ( x )=35 11. lim x 0 f ( x ) does not exist Continuity 1. Set f ( x 2 x 2 - 1 < 2 A, x =2 x 3 Bx, x > 2 . Find A and B so that f will be continuous at x . Ans: A =7 ,B = - 1 4 2. Set f ( x x 2 - 2 x - 3 x 3 - 9 x . (a) Determine the intervals on which f is continuous. Ans: ( -∞ , - 3) , ( - 3 , 0) , (0 , 3) , (3 , ) (b) What is lim x →- 3 + f ( x )? Ans: does not exist (c) What is lim x 3 f ( x )? Ans: 2 9 3. Set f ( x 2 x - 1 - 3 x - 5 . Defne f at x = 5 so that f is continuous at 5. Ans: 1 3 II. DERIVATIVE 1. (a) Use the defnition o± the derivative to calculate f ± ( x ) where f ( x )=1 - 4 x x 2 Ans: f ± ( x - 4+4 x 1
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(b) Let
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ans-C-1-Ex1-F07 - MATH 1431 EXAM 1 REVIEW I. LIMITS...

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