F g f g

le above gives values of the functions and their first derivatives as selected values of x. The function h is given by the equation h(x) = f(g(x))-6 b) find the rate of change of h for the interval 1>x>3. Graph in picture

ble above gives values of the functions and their first derivatives as selected values of x. The function h is given by the equation h(x) = f(g(x))-6 a) find h’(3) b) find the rate of change of h for the interval 1>x>3. Graph in picture

hoots a laser beam in a straight path from a deck 14 feet above sea level off the coast of Florida, is it possible the laser beam will cross the path of the model rocket? Use a piece of graph paper to write/model equations f ( x ) to represent the path that models the rocket and g ( x ) to represents the path that models the laser beam.

, ACD®B, D®EF, BE®C, CF®BD, CE ®AF). (a) Find (BD)+ (b) Find (AB)+ (c) Find Candidate Keys for R Question 3 Given the scheme R= (ABC), and following set of functional dependencies: F = (A®BC, B® AC, C ® AB). (a) Find closure (BC, F) (b) Find at least one candidate key for R. (c) Find at least one super-key for R which is not the same as your answer in (b). (d) Find at least one minimal cover for a relational scheme (ABC). Show work. (e) Provide a 3NF decomposition for R. Question 4 Consider the following set of FDs: F = (A ® B, AB ® C, D ® AC, D ® E) G = (A ® BC, D ® AE) H = (A ® BC, B ® C, A ® B, AB ® C, AC ® D). (a) Is F ≡ G? Show your work. (b) Find the minimal cover for H. Show work.

er-example (if false). (a) If |f | is integrable on [a, b], then f is also integrable on [a, b]. (b) If f = F ′ for some function F on [a, b], then f is continuous on [a, b]. (c) If g is continuous on [a,b], then g = G′ for some G on [a,b]. (d) If G(x) = ???? x g is differentiable at p ∈ (a, b), then g is continuous at p.

1 ? (Without using differentiation rules) For each statement, explain why it must be true, or use an example to show that it can be false. a)If y = f ( x ) has a horizontal tangent line at x = 1 then y = g ( x ) , where g ( x ) = f ( x − 1 ) + 1 , has a horizontal tangent line at x = 2 . b)A tangent line always has exactly one point in common with the graph of the function.

ave a horizontal tangent line at x = 1 ? (Without using differentiation rules) For each statement, explain why it must be true, or use an example to show that it can be false. a)If y = f ( x ) has a horizontal tangent line at x = 1 then y = g ( x ) , where g ( x ) = f ( x − 1 ) + 1 , has a horizontal tangent line at x = 2 . b)A tangent line always has exactly one point in common with the graph of the function.