Fervs - CALCULUS 1 FINAL EXAM REVIEW SOLUTIONS x 10 x < 4 f(x = x 4 6 = x 2 x 4 x 2 w x = domain set up a sign graph with 2 and 0 on it Get the x(x

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CALCULUS 1: FINAL EXAM REVIEW SOLUTIONS 1. f x ( 29 = x + 4 - 6 = 10, 4 2, 4 x x x x - - < - - ≥ - 2. w x ( 29 = x x + 2 domain: set up a sign graph with –2 and 0 on it. Get the x/(x+2) is > 0 if x < -2 or x > 0 the domain. For the range, if you set [ 29 ( 29 2 2 2 2 0 , 1 2 2 1 0 1 0,1 1, x x y y note that y then y solve for x so y x x y so the range is y and y or = = = + + - ≠ ≠ +∞ 3. a) ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 2 2 3 4 3 4 2 3 2 3 2 3 x h x h x x f x h f x h x h xh h h x h h h h h + - + + - - + + - + - + - = = = = + - b) ( 29 ( 29 0 lim 2 3 2 3 h x h x f x + - = - = , the derivative with respect to x of f(x) 4. Given f x ( 29 = x - 5 and g x ( 29 = x find f r g ( 29 x ( 29 and g r f ( 29 x ( 29 and the domains of all 4 functions. [ 29 [ 29 5, , 0, f g D D = +∞ = +∞ ( 29( 29 ( 29 [ 29 5 , 25, f f g x f x x D = = - = +∞ r ; ( 29( 29 ( 29 [ 29 5 5 ; 5, g f g f x g x x D = - = - = +∞ r r 5. a) f x ( 29 = x 2 , x < 1 2 x , x 1 ( 29 , f D = -∞ +∞ discontinuity at x = 1 since 2 1 1 lim 1 but lim 2 2 x x x x - + = = [ 29 0, f R = +∞ b) ( 29 2 2 3 1, 3 3 x x g x x x x - - = = + - ( 29 ( 29 ,3 3, g D = -∞ +∞ discontinuity at x = 3 ( 29 ( 29 ,4 4, g R = -∞ +∞ 6. a) ( 29 ( 29 2 2 0 0 2 2 lim lim 2 2 1 2 x x x x x x x x x x + + = = - - b) 3 3 3 3 2 1 lim lim 4 3 7 7 7 x x x x x x x x →+∞ →+∞ + = = - + - - c) 2 lim 2 x x x + - = -∞ - d) 2 0 0 3 sin 4 sin 4 lim lim 3 4 4 4 x θ + = + =
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7. a) ( 29 ( 29 2 2 2 2 1 sin 1 sin cos lim sec tan lim lim lim 0 cos cos cos sin 0 0 x x x x x x x x x x x x x π - - - - - - - = - = = = - -∞ - -∞ b) ( 29 ( 29 ( 29 ( 29 ( 29 2/ 2/ 2/ 2ln 2 lim ; ln ln ln x x x x x x x x x x e x e y x e y x e x e x x →+∞ + + = + = + = + = ( 29 ( 29 2 2 1 2ln 2 2 lim lim lim lim 2; ln 2; 1 1 x x x x x x x x x x x e x e e e x e y y e x e e →+∞ →+∞ →+∞ →+∞ + + + = = = = + c) ( 29 ( 29 2 2 0 0 0 0 sin ln cos tan sec 1 cos lim lim lim lim 3sin3 ln cos3 3tan3 9sec 3 9 cos3
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This note was uploaded on 12/26/2011 for the course MAC 2311 taught by Professor Staff during the Fall '08 term at FIU.

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Fervs - CALCULUS 1 FINAL EXAM REVIEW SOLUTIONS x 10 x < 4 f(x = x 4 6 = x 2 x 4 x 2 w x = domain set up a sign graph with 2 and 0 on it Get the x(x

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