For the following problems, use the fact that the derivative of f(x) = r . In(x) is f'(x) = In(x) + 1.13. Use Newton's method to find a root of the function f(x) = 12 -26 starting with ro = 5. What are $1 and +2 to 3 decimal places?21. A perfectly circular lake begins freezing starting from the shore. Ice develops evenly around the perimeter of the lake, so there is always a central circle of water. If the ice grows at a rate of 5 square meters per hour, how quickly is the radius of the unfrozen portion of the lake decreasing when the radius is 20 meters?22. Given the following table of values for a function f on [0,3], what are the left, midpoint, and right Rie- mann sums with 3 subintervals for the function? What is the right Riemann sum with 6 subintervals? 0 0.5 1 1.5 2 2.5 3 f (x) -2 -1.5 -0.5 0.5 2 425. A rectangular card must have a total area of 20 in'. There is a printed area in the center with blank margins on the left and right of 1 inch each and top and bottom margins of = inch each. What dimensions of the card maximize its printed area?28. Find the net, oriented area under the curve y = 4r - 6: + 3 between r = 1 and r = 4. 100 29. What is the value of K? k=11. The velocity of an object is given by v(t) = -6t + 5. (a) What is the acceleration of the object as a function of t? (b) What is the average velocity of the object on the interval [1, 3]? (c) What is the position of the object as a function of t if the object has position 3 when t = 1? 2. The graph of the function f is given below. (a) What is lim f(x)? 10 (b) Is f continuous at r = -2? (c) What is f'(-1)? 5- (d) What is f(x) da? (e) Is f differentiable at r = 1? (f) What is lim f(a)? -5 0 5 (g) Is f differentiable at r = 3? (h) Which is the largest? (Choose exactly one) 10 or f(x)dx or f(x)dr