A graphing calculator ls required for the following problem. Let x) = log(x2 + 1), g(x) = 10 x2. and R be the region bounded by the graphs of f and g, as shown above. a) Find the volume of the solid generated when R is revolved about the horizontal line y = 10. b} Region R is the base of a solid. For this solid, each cross section perpendicular to the xaxis is an isosoeles right triangle with a leg in R. Find the volume of the solid. s) The horizontal line y = 'l divides region R into two regions such that the ratio of the area of the larger region to the area of the smaller region is 3:1. Find the value of k. A graphing calculator ls required for the following problem. A grain elevator lls each railcar of a train with grain. The number of railcars lled after t hours is given by a differentiable function R for 0 S t S 15. Values ofR(t) at various times tare given in the table above. a} Use the data in the table to approximate the rate at which the number of lled railcars is changing at time t = 5. Show the computations that lead to your answer. Indicate units of measure. b) Will the instantaneous rate at which the number of lled railcars is changing at some time t be equal to the approximation in part (a)? Justify your answer. 6) Use a trapezoidal sum with the four subintervals indicated in the table to estimate if? R(t)dt. Using correct units. interpret the meaning of 115_f015R(t)dt in the context ofthis problem. d) Determine flmRthdt. Using correct units, explain the meaning of the expression in the context of this