Test2_solutions - Math 1432 Exam 2 Review KEY 1 f x = 3x 2...

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Math 1432 Exam 2 Review - KEY 1. a. 2 11 / 3 '( ) 3 0 for all x => f(x) is always increasing => one-to-one () ( 1 ) fx x x = = b. 1 3 0 for all x => f(x) is always increasing => one-to-one 10 () 3 x => = c. 2 '( ) => not one-to-one 9 x x = 2. 1 7 ' ( 1 ) 2 f = . 3. 2 7 4. 1 12 5. Find the derivative: a. ( ) 4 ' 24 x x e y ex + = + b. ( ) 6 6 'c o s l n ( 5 ) 5 yx x ⎛⎞ = ⎜⎟ ⎝⎠ c. 22 2 '2 2 2 xx e x e =+ + d. c o s h ( 3 )3 s i n h ( 3 ) e x e x e. tan 2 x x = f. 4 6 2 xe xe = g. [ ] (7 ) '( c o s) l n ( c o s)( 7 ) t a n x x x x + = h. 26 61 8 (3 1) 2 ln(3 31 x x x x x + + ⎡⎤ = + ⎢⎥ ⎣⎦ i. 6 2 6 1( 52) x e +
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j. 2 '( ) ln 7 fx x = k. ( )( ) 2 '2 l n 6 6 x y = l. 2 6 6 14 x x = + 6. Integrate: a. 4 1 ln 4 e e dx x = b. 2 99 csc 1 1 ln | 2 5cot | 25 c o t 5 9 xx x ed x x e C x ⎛⎞ = + ⎜⎟ + ⎝⎠ c. 2 sinh 1 (2 cosh ) 2 cosh x dx C = + ++ d. 2 x x e dx e C x =+ e. ( ) 2 4ln|3 | 3 dx x C = + f. 2 ln | 1| 1 x dx x x C x + + g. 2 2 2 33 3 3 3l n ( 1 ) 12 dx x x C x + + + h. 32 2 cos sin sin tan cos dx x x x C x = + + i. 1 tan(3 ) ln | sec(3 ) | 3 xdx x C j. 2 2 arctan(3 ) 1 (arctan(3 )) 19 6 x dx x C x + k. 3 2 2 0 1 3 1 dx x π = l. 43 5 7 11 cos sin cos cos 57 d x x x C = + + m. 52 3 5 7 121 cos sin sin sin sin 357 d x x x x C = + + n. 1 cot cot ln | sin | 2 xdx x x C = + o. 22 ln(2 ) ln(2 ) 24 d x x C =
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p. 22 2 sin(3 ) cos(3 ) sin(3 ) 39 xx d x x x x C = + + q.
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Test2_solutions - Math 1432 Exam 2 Review KEY 1 f x = 3x 2...

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