Please solve and show work for these 6 questions:

HW4: Problem 1 Previous Problem Problem List Next Problem (1 point) Use algebra to evalute the following limit. lim (3+h) 2-9 = h-0 hHW4: Problem 2 Previous Problem Problem List Next Problem (1 point) Use algebra to evalute the following limit. lim (3+h)3-27 h-0 hHW4: Problem 3 (1 point) Estimate f ' (6) for f (x) = 2". Be sure your answer is accurate to within 0.1 of the actual value. f'(6)a\" Be sure that you can explain your reasoning. HW4: Problem 4 (1 point) Consider the function y = f (x) graphed below. Give the x-coordinate of a point where: A. the derivative of the function is positive: x = B. the value of the function is positive: x = C. the derivative of the function is largest: x = D. the derivative of the function is zero: x = E. the derivative of the function is approximately the same as the derivative at x = 1.25 (be sure that you give a point that is distinct from x = 1.25!): x = HW4: Problem 5 Previous Problem Problem List Next Problem (1 point) Consider the graph of the function f(x) shown below. 2 5 Using this graph, for each of the following pairs of numbers decide which is larger. Be sure that you can explain your answer. A. f (3) ? ~ f (4 ) B. f (3) - f(2) ? ~ f(2) - f(1) C. f(2)-f(1) ? v f (3) -f(1) 2-1 3-1 D. f'(1) ? ~ f'(4)