calculus_practice exam - NON-CALCULATOR SECTION 1(8 points...

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Unformatted text preview: NON-CALCULATOR SECTION: 1. (8 points) Use the limit definition of a derivative to find the derivative of f ( x ) = 2 x 2- 2. f ( x ) = lim h → f ( x + h )- f ( x ) h = lim h → (2( x + h ) 2- 2)- (2 x 2- 2) h = lim h → (2 x 2 + 4 xh + 2 h 2- 2)- (2 x 2- 2) h = lim h → 4 xh + 2 h 2 h = lim h → 4 x + 2 h = 4 x 1 2. (8 points) Solve the following for x : 7 x +2 = e 17 x ln 7 x +2 = ln e 17 x ( x + 2) ln 7 = 17 x x ln 7 + 2 ln 7 = 17 x- 17 x + x ln 7 =- 2 ln 7 x (- 17 + ln 7) =- 2 ln 7 x =- 2 ln 7- 17 + ln 7 2 3. (5 points) Find a possible equation for the following function.- 3- 2- 1 1 2 3 4 5 6 x- 2 2 4 6 8 10 y Zeros at x =- 2 , 3 and 5 give factors of ( x +2)( x- 3)( x- 5) . We know this is a cubic, so now we need only find the constant in front, using the y-intercept. f ( x ) = c ( x + 2)( x- 3)( x- 5) f (0) = c (2)(- 3)(- 5) = c (30) We want f (0) = 7 , thus, c = 7 30 . So, our function is f ( x ) = 7 30 ( x +2)( x- 3)( x- 5) . 4. (3 points) Which graph in the figure below best matches each of the following stories? time distance from home time distance from home I II time distance from home time distance from home III IV (a) I had just left home when I realized that I had forgotten my books and so I went back to pick them up. IV (b) Things went fine until I had a flat tire. II (c) I started out calmly and sped up when I realized that I was going to be late. III 3 5. If g ( x ) = 4- x 2 x 2 + 2 x (a) (2 points) State the domain of g ( x ). Domain is all real numbers except where the denominator is zero, which is at x = 0 and x =- 2 . (b) (2 points) Find g (1). g (1) = 4- 1 2 1 + 2 = 1 (c) (2 points) Solve g ( x ) = 2. 2 = 4- x 2 x 2 + 2 x 2( x 2 + 2 x ) = 4- x 2 3 x 2 + 4 x- 4 = 0 (3 x- 2)( x + 2) = 0 This occurs when x = 2 3 and when x =- 2 , however, x =- 2 is outside of our domain for this function. Therefore, the only solution is whenof our domain for this function....
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This note was uploaded on 04/30/2011 for the course MATH 205 taught by Professor Tseng during the Spring '08 term at American College of Computer & Information Sciences.

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calculus_practice exam - NON-CALCULATOR SECTION 1(8 points...

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