1. Consider function f: R R defined by f(x) = e A. Determine the intervals on...

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1. Consider function f: R R defined by f(x) = e A. Determine the intervals on which function f is increasing/decreasing. B. Determine the intervals on which function f is concave up/down. C. Find the ordered pairs (x, f(x)) for all critical points and points of inflection. D. Sketch a graph of function . 2. Evaluate the definte integral S 2 In 3 xe e-x/2. 4. Evaluate the following indefinite integrals. 2 A. S x 3x dx. B. S x log3 (x) dx. x /2 dx. 3. Consider the functions (x) = e, 2(x) = e, and 3 (x) = e. Call the region of Quadrant I completely enclosed by these three functions by Region R. A. In Quadrant I: functions and have one intersection point; functions and 3 have one intersection point; functions and have one intersection point. Find the x-coordinates of these three intersection points. B. Labeling the three x-coordinates from Part A as a < b < c: on the interval [a, b], two of these three functions are the "top" and "bottom" functions defining Region R; on the interval [b, c], two of these three functions are the "top" and "bottom" functions defining Region R. Identify the "top" and "bottom" functions defining Region R on the intervals [a, b] and [b, c]. C. Sketch a graph of Region R. D. Use your result from Part A, B, and C to find the geometric area of Region R. 1. Consider function f: R R defined by f(x) = e A. Determine the intervals on which function f is increasing/decreasing. B. Determine the intervals on which function f is concave up/down. C. Find the ordered pairs (x, f(x)) for all critical points and points of inflection. D. Sketch a graph of function . 2. Evaluate the definte integral S 2 In 3 xe e-x/2. 4. Evaluate the following indefinite integrals. 2 A. S x 3x dx. B. S x log3 (x) dx. x /2 dx. 3. Consider the functions (x) = e, 2(x) = e, and 3 (x) = e. Call the region of Quadrant I completely enclosed by these three functions by Region R. A. In Quadrant I: functions and have one intersection point; functions and 3 have one intersection point; functions and have one intersection point. Find the x-coordinates of these three intersection points. B. Labeling the three x-coordinates from Part A as a < b < c: on the interval [a, b], two of these three functions are the "top" and "bottom" functions defining Region R; on the interval [b, c], two of these three functions are the "top" and "bottom" functions defining Region R. Identify the "top" and "bottom" functions defining Region R on the intervals [a, b] and [b, c]. C. Sketch a graph of Region R. D. Use your result from Part A, B, and C to find the geometric area of Region R.