please solve questions 1-15! Thank you!

1. Evaluate E (3k + 1) . (5 points) 126 O 124 O 120 O 83 x . -25X52 2. Use geometry to evaluate J f(x)dx where f(x) = 2, 2 0. Find the value of b so that the area of the region R is 288 square units. (5 points) O 16971 () 16.478 O 12 O s 8. The base of a solid is bounded by the curve y = Jx +2 . the x-axis and the line x = 1. The cross sections, taken perpendicular to the x-axis, are squares. Find the volume of the solid. (5 points) O o5 O 3.464 O 45 O None of these 9. Find the average value of y = J64 x? . on its domain. (5 points) O = o O 2 O 4 10. Find the domain for the particular solution to the differential equation % e , with initial condition y(2) = 2. (5 points) y O x>-2 O [2V2.22] O a4 O All real numbers 11. The slope field for a differential equation is shown in the figure. Determine the general solution of this equation. (5 points) O y=CX2 O x=Cy2 O x2- y2 = C2 O x2 + y2 = C2 12. The function f is continuous on the interval [4, 15], with some of its values given in the table above. Estimate the average value of the function with a Trapezoidal Approximation, using the 4 intervals between those given points. (5 points) x 4 9 11 14 15 f(x) -6 -11 -18 -21 -25 -12.727 O -11.546 O -16.273 O -13.90913. If the graph of f'(x) is continuous and decreasing with an x-intercept at x = c, which of the following must be true? (5 points) O The graph of f has a relative maximum at x = C. O The graph of f has an inflection point at x = c. O The graph of f has a relative minimum at x = c. O None of the above is necessarily true. 14. Which of the following shows that f(x) grows at the same rate as g(x)? (5 points) O lim T(X) = 1000 x-cog(X) O lim 1(X) = 0 x-> g(x) O f(x ) lim = 00 x- g(x) O None of these 15. Find F '(x) for F(x) = cos(t4 )dt . (5 points) O cos(1) - cos(x12) -3x2cos(x 12) O cos(x7) O -cos(x12)