MAC2233-AN4

# MAC2233-AN4 - MAC2233 Survey of Calculus Practice Test#4 1...

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Survey of Calculus MAC2233 Practice Test #4 1) Identify the correct sketch of the graph of : a) b) i) x e y = A ii) x e y = C iii) x ln - = y D___ iv) x ln = y B c) d) 2) Solve for x: a) 4 = e x 2 ln b ) 6 = 2 x - 1 2 4 2 x x = (1 )ln 2 ln 6 ln2 ln2 ln6 ln6 ln2 1.585 ln2 x x x −= == c) 0 = 6 - e 1 - 2x d ) 3 = 2 x 1 - x 21 ln l n 6 ln6 1 1.396 2 x e x x = + 1 ln3 ) l n 2 l n 3 ln2 ln3 1.710 xx x = = =− e) 3000 = ) 12 .07 + 1 1000( 12x f) 24 = e - 1 45 2x - 12 .07 ln 1 12 .07 (12 )ln 1 12 15.74 .07 12ln 1 12 x x x ⎛⎞ += ⎜⎟ ⎝⎠ + 2 2 45 1 24 45 21 1 24 24 21 2l n 24 21 ln 24 .. 2 x x e e x xd n e =

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3) Differentiate with respect to x: a) e x = y x 2 2 b ) ) (2x ln = y 2 22 2 2 2 '( 2 ) 2 '2 ( 1 ) xx x y xe x e x yx e x =⋅ + =+ 2ln2 1 '2 ( ) ( 2 ) 2 2 ' y x y x y x = = = c) 2x x ln = y 2 d ) 1 + e 1 - e ln = y x x 2 2 ln 1 ()l n( 1 ) ' 1l n ' x y x x y x x y x = = = 2 ln( 1) ln( 1) 11 (1 )(1 ) ) ) 2 ' 1 x x ye e ee y y e y e =− −+ +− ′ = = e) e x = y x 2 2 f ) x xe y = x 1-e 2 2 2 2 1 2 2 2 2 2 2 () ) 1 ) ) x x x x e e e x e yex x + 2 2 2 2 2 2 2 2 (1 )( )( 1) ( ) ' ) (1 )( ) ' (1 ) ' (1 ) ' ) ) ' ) x x x x x x x x x x x x x eex x e e y e ex x e y e xe e xe e xe y e xe e e y
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MAC2233-AN4 - MAC2233 Survey of Calculus Practice Test#4 1...

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