Name: 1. Find the derivatives of the following functions in terms of the derivatives of the functions F, G and H. [F(x2) - 10] = [20 - G(sin(x))] = [H (e") - H(In(1))] = 2. You want to purchase a heater for your outdoor pool. The salesperson advises that to purchase the correct size heater you must know the approximate surface area of your pool. You and a friend take measurements every 5 meters and collect the lengths (in meters) given in the diagram below. Explain several ways that you could use this information to approximate the surface area of your pool. 5.6 5.0 4.8 6.8 7.2 4.8 6.23. A rectangular diving pool 5m wide and 12m long has a curved bottom. The depth of the pool in meters is given by M55) = 41.019: i mm: + 5) + 6 where cc is the distance in meters from the shallow end of the pool and 0 S :5 S 12. Estimate the volume of the pool in the following two ways. 0 Using a right Riemann sum with 3 subintervals. 0 Using a left Riemann sum with 4 subintervals. 4. From the given table compute the following Riemann sums. f(g:)52114 o The left sum With n = 3 I The right sum With n = 3 o The midpoint sum with n : 3 5. Consider the function f (3:) : 2 7 3:2 over the interval [1, 3]. Use summation notation to express the right Riemann sum with 50 subintervals. 6. Suppose the right Riemann sum R100 has been found to be given by the expression we , k 1 R100 : gsm (5 + 20) E. Determine the function f (x) the interval [(1, b], and the number of rectangles 71 used in the calculation of this Riemann sum. 7. Express the limit Tl. . . 2 a: nlggogsm (2711:\" A33 as an integral over the interval [0, 1]. 8. Evaluate the integral of the piecewise dened function graphed below on the interval [0,12]. Use geometry formulas for the areas of triangles and circles, and remember to subtract the areas below the maxis