MAC2233-ANF

# MAC2233-ANF - Survey of Calculus Practice Final Determine...

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Survey of Calculus MAC2233 Name___________________ Practice Final FINAL EXAM Section__________________ Determine the following: 1) 5 + x 5x x lim 2) 6 - x + x 3 + x 2 x 2 3) 4 - 2x + x 3 - x 5 -1 x 2 3 4) Use the definition of derivatives to find the derivative of 5 + 2x + x 3 = f(x) 2 hh h f x h f x x h x h x x x xh h x h x x h xh h h x h x h       22 00 2 2 2 0 2 ( ) ( ) 3( ) 2( ) 5 (3 2 5) lim lim 3 6 3 2 2 5 2 5 lim 6 3 2 lim lim6 3 2 6 2 Find the derivatives of the following functions: 5) x 3 - x + x 4 = y 3 5 6) ) 5 + 12x - x (2 = y 3 2 1 44 2 4 4 1 ' 20 9 2 19 ' 20 2 y x x x yx x x 7) ) 4 - x (3 x = y 4 2 5 8) x ln = y 2 5 2 3 2 4 4 4 2 3 2 2 4 2 3 2 ' 4(3 4) (6 ) (3 4) 5 ' (3 4) [24 (3 4)5] ' (3 4) (39 20) y x x x x x y x x x x y x x x 1 2 1 2 (2ln ) 1 2 1 ' (2ln ) ( ) 2 2ln x x xx  9) ) 7 - (3x ) 1 - (2x = y 2 3 10) e 5 = y 2 + 7x   2 2 3 4 2 4 2 3 (3 7) (3)(2 1) (2) (2 1) 2(3 7)(3) ' (3 7) 6(3 7)(2 1) 3 7 (2 1) ' (3 7) 6(2 1) ( 6) ' (3 7) x x x x y x x x x x y x y x    32 5( 1) 3( 1) 2( 1) 4 14  lim 3 ( 2)( 3) lim 1 .. ( 2) x x 2 x x d n e x 2 x  5 lim 5 5 1 x x  ' 3(2 12 5) (4 12) ' 12( 3)(2 12 5) ' (12 36)(2 12 5) y x x x y x x x y x x x 7 2 7 2 ' 5 (7) 35 y e e

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11) Find the equation of the tangent line of the curve x = y at x = 1. 1 2 11 22 1 1 1 '1 2 2 2 (1,1) 1 2 y x x y x slope yx point m slope   () 1 1 ( 1) 2 21 y y m x x or xy      12) Find all points where the tangents to the curve 32 + +1 y - x xx are horizontal. 2 ' 3 2 1 0 (3 1)( 1) 1 ,1 3 1 22 int , ( 1,2) 3 27 y x x Po s and          13) For 3 + x + x 2 - x = f(x) 2 3 determine: a) All relative maximum and minimum points b) The intervals of increase and decrease.
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MAC2233-ANF - Survey of Calculus Practice Final Determine...

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