MAC2233-AN1 - MAC2233 Survey of Calculus Determine whether...

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Survey of Calculus MAC2233 Practice Test #1 Determine whether each of the following functions is: a) a function. (Note: you may use more than one letter) b) a one to one function c) a continuous function d) a differentiable function 1) ___ A , B _______ 2) ___ A , C , D _______ For the functions f (x) and g (x) above, answer the following: 3) Find the Domain of f (x) 4) Find the Domain of g (x) ( , ) ( , ) 5) Find the Range of f (x) 6) Find the Range of g (x) ( , 1 (1, ) 1, ) 7) f (1) = 1 8) g (1) = 0 9) Find 1 lim x f (x) . . d ne 10) Find 1 lim x g(x) 0 11) Find lim x f (x) ; . . . d ne 12) Find lim x g(x) ; . . d ne 13) Is f (x) continuous at x = 1 14) Is g (x) differentiable at x = 1 no yes
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Find each limit, if it exists. 15) lim 2 3x - x 0 x 0 3 lim . . x d n e x 16) lim 2 + 5 x x -2 2 ( 2) 5 3 17) 5 6 3 3 lim 2 + x + x x + x - 18) 5 4 2 x 2 3 2 7 3 lim x x x x 3 3 ( 2)( 3) lim lim( 2) 1 ( 3) x x x x x x 2 5 4 2 lim 85 3( 2) 2( 2) ( 2) 7( 2) 3 x 19) 6 4 12 2 lim 2 x + + x x x 20) 2 4 2 2 2 x 2 lim x x x 2 4 2 2 2 2 2 6 1 lim 2 2 12 2 x 2 2 ( 6) 1 lim lim . . . ( 2)( 6) ( 2) x x x d n e x x x Find the slope of the tangent line for: 21) y = 2x 2 - 4x 22) 2 3 y x 0 2 2 0 2 2 2 0 ( ) ( ) lim 2( ) 4( ) (2 4 ) lim 2 4 2 4 4 2 4 lim 4 4 h
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