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Math 151 Exam I A F 10

# Math 151 Exam I A F 10 - x x x f has an x-intercept 7 a...

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MATH 151 EXAM IA NAME ___________________ Mrs. Bonny Tighe 2.1-2.8 150 points Section_______ Mon 9/27/10 1. State and use the definition of the derivative to find f ’(x) for 2 3 ) ( - = x x f 2. Evaluate the indicated limit, if it exists. _ __________ ) 5 ( 5 lim a) 2 2 0 h = + - - - h h ____ __________ 3 9 lim b) 2 2 0 = - + x x x ____ __________ 3 12 4 lim c) 3 = - - + x x x

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3. a) _____ lim 2 = - x x e b) __________ 5 4 3 2 lim 2 = - + x x x ______ tan lim ) 1 = - x c x d) ____ __________ 9 1 2 5 lim 2 = + - x x x 4. a) What must be true for a function f(x) to be continuous at a point x = a ? b) Find the numbers at which f is discontinuous. At which of these numbers is f continuous from the right, from the left, or neither? - < < + = 3 3 3 1 1 1 1 ) ( x if x x if x x if x x f 5 a) For what value of the constant c is the function f continuous on (- , )? - < - = 3 4 3 2 ) ( 2 x if cx x if cx x f b) What must be true for a function to be differentiable at a point?
6. State and use the intermediate Value Theorem so show that the function 1 5 2 )

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Unformatted text preview: x x x f has an x-intercept. 7. a) Find the equation of the tangent line to the curve 3 3 ) ( x x f-= when x = 2. You must you the definition of derivative. b) Let ) ( t P be the percentage of Americans under the age of 18 at time t years. What is the meaning of ) ( ' t P ? What are its units? 8. State and use the Formal Definition of a Limit to symbolically find δ in terms of ε . 4 ) 3 2 ( lim 2-=-→ x x 9. a) The graphs of a function f is given. Graph f '. b) Find the horizontal/ slant asymptote for the function 3 4 2 5 3 2 ) ( 2 2 3 + +-+-= t t t t t t f 10. a) Find an equation of the tangent line to the graph of y = g ( x ) at x = 4 if g ( 4 ) = −3 and g' ( 4 ) = 5 . b) If the tangent line to y = f ( x ) at ( 7 , 4 ) passes through the point (0, 3 ), find f ( 7 ) and f ' ( 7 )....
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