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# my custom review - silva(jrs4378 My Custom Review...

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silva (jrs4378) – My Custom Review – gualdani – (56455) 1 This print-out should have 66 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Determine d 2 y/dx 2 when 3 x 2 + y 2 = 5 . 1. d 2 y dx 2 = 15 y 3 2. d 2 y dx 2 = 15 y 3 3. d 2 y dx 2 = 3 y 3 4. d 2 y dx 2 = 15 y 2 5. d 2 y dx 2 = 15 y 2 002 10.0 points Use continuity to evaluate the limit lim x 4 π sin ( x + 4 sin x ) . 1. limit = 1 2. limit = 1 3. limit = 4. limit = 0 5. limit = 4 π 003 (part 1 of 3) 10.0 points (i) Determine the value of lim x 2+ x 7 x 2 . 1. none of the other answers 2. limit = 3. limit = 7 2 4. limit = 7 2 5. limit = −∞ 004 (part 2 of 3) 10.0 points (ii) Determine the value of lim x 2 x 7 x 2 . 1. limit = 7 2 2. none of the other answers 3. limit = 4. limit = 7 2 5. limit = −∞ 005 (part 3 of 3) 10.0 points (iii) Determine the value of lim x 2 x 7 x 2 . 1. limit = −∞ 2. limit = 3. limit = 7 2 4. none of the other answers 5. limit = 7 2 006 10.0 points Find all vertical asymptotes of the graph of y = 2 x 2 x 1 4 x 2 7 x + 3 .

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silva (jrs4378) – My Custom Review – gualdani – (56455) 2 1. x = 1 2. x = 3 4 , 1 3. x = 3 4 , 1 4. x = 3 4 , 1 5. x = 3 4 007 10.0 points Below is the graph of a function f . 2 4 2 4 2 4 2 4 Use the graph to determine lim x 3 f ( x ). 1. lim x 3 f ( x ) = 3 2. lim x 3 f ( x ) = 2 3. lim x 3 f ( x ) = 4 4. lim x 3 f ( x ) does not exist 5. lim x 3 f ( x ) = 1 008 10.0 points Simplify the expression f ( θ ) = 5 sin 4 θ cos 2 θ 3 sin 2 θ . 1. f ( θ ) = 5 cos 2 θ + 3 sin 2 θ 2. f ( θ ) = 2 sin 2 θ 3. f ( θ ) = 7 sin 2 θ 4. f ( θ ) = 5 cos 2 θ 3 sin 2 θ 5. f ( θ ) = 8 sin 2 θ 6. f ( θ ) = 13 sin 2 θ 009 10.0 points Find the second derivative, d 2 y/dx 2 , when 6 x 3 + 3 y 2 = 7 . 1. d 2 y dx 2 = 2 x (2 y 2 + 3 x 3 ) y 3 2. d 2 y dx 2 = 2 x ( y 3 + 3 x 2 ) y 2 3. d 2 y dx 2 = 2 x ( y 3 3 x 2 ) y 2 4. d 2 y dx 2 = 3 x (2 y 2 3 x 3 ) y 3 5. d 2 y dx 2 = 3 x ( y 3 + 3 x 2 ) y 2 6. d 2 y dx 2 = 3 x (2 y 2 + 3 x 3 ) y 3 010 10.0 points Use properties of logs to simplify the ex- pression log 9 ( x radicalbig x 2 63 ) + log 9 ( x + radicalbig x 2 63 ) . 1. 9 + log 9 7 2. log 9 7
silva (jrs4378) – My Custom Review – gualdani – (56455) 3 3. 1 + log 9 7 4. 1 + log 7 9 5. log 7 9 011 10.0 points Determine which (if any) of the following functions is not continuous at x = 7. 1. f ( x ) = braceleftBigg 28 2 x 7 x negationslash = 7 4 x = 7 2. f ( x ) = braceleftbigg | x 7 | x negationslash = 7 0 x = 7 3. f ( x ) = 1 x 1 x 7 1 6 x < 7 4. f ( x ) = 1 | x 1 | x 7 1 6 x < 7 5. all continuous at x = 7 6. f ( x ) = braceleftBigg 1 x 7 x negationslash = 7 7 x = 7 012 10.0 points If y = y ( x ) is defined implicitly by 4 y 2 xy 12 = 0 , find the value of dy/dx at (8 , 3). 1. dy dx vextendsingle vextendsingle vextendsingle (8 , 3) = 3 16 2. dy dx vextendsingle vextendsingle vextendsingle (8 , 3) = 3 16 3.

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