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CALCULUS BC TEST ON 4.6, 5.1 – 5.2, & FUNCTIONS DEFINED BY INTEGRALS NAME_____________________________ PERIOD____DATE__________________ 1. Suppose that g is an even continuous function and that g 2 4 and 2 g ' x dx 14 5 2 Find g 5 . _______________________________________________________________________________ 2. A bowl of soup is placed on the stovetop. The temperature of the soup at selected times is given in the table below. x (min.) T x (° F) 0 94 4 112 (a) Use data from the table to find 7 122 12 154 0 T x dx . 7 (b) What is the average temperature of the soup in the 12 minute interval. Use a right side Riemann sum to calculate. (c) Estimate the value of T 5 Explain what this value represents and include units. (d) (Extra Credit) Estimate the value of (T 1 ) '(100) ________________________________________________________________________________ Multiple Choice. Write your answer in the blank. _____ 3. Let g be the function given by g x 100 t 2 5t 4 e t dt . Which of the x 2 1 following statements about g must be true? I. g is decreasing on (1,4). II. g is increasing on (,1) U (4, ) . III. g 1 0 1 (A) I only (B) II only (C) III only (D) II and III only (E) I, II, and III dy . dx 4. x tan xy y 3 5 Find cos x 5. y ln x2 6. [tan x sec( x) ]dx _____________________________________________________________________________ Evaluate. 4 4x 4 dx 7. 0 x2 2x 8. e3 1 ln x dx x Multiple Choice. Show your work, and write your answer in the blank. _____ 9. If F x (A) 1 (B) 1 2 t 2 dt , find the value of F . 4 3 1 (C) (D) (E) 1 2 2 sin x 0 (F) 3 4 ln( x 3) . Find the x-coordinate of the critical point(s) x3 of f, and determine whether this point is a relative minimum, a relative maximum, or neither for the function f. Justify your answer. 10. Let f be the function given by f x ________________________________________________________________________________ 11. The graph of the function f shown in the figure consists of two line segments. Let g be the function x given by g x f t dt . Justify in a sentence. 3 (a) Find g 4 , g 4 , and g 4 . f (x) (b) For what value(s) of x in the open interval 2, 5 does the graph of g have a point of inflection? Justify. (c) For what value(s) of x in the open interval Justify. 2, 5 does g have a relative min? (d) Find the absolute maximum for the function g. Justify (e) Find d g x ( ) at x = 1 dx x