help

1. Use the limit definition of the derivative to nd g'(x) ifg(x) = 2x2 6x + 13. 2. Use a Riemann sum to estimate the value of EU) - y2)dy as follows: subdivide the interval into four equal subintervals, and let the sample points 3/? be the right endpoints of the subintervals. 3. (a) State the Mean Value Theorem. Be sure to include the hypotheses and conclusion of the theorem. (ID) Find all c that satisfy the conclusion of the Mean Value Theorem for the function f(x) = 2x3 5x2 - 10x + 5 in the interval [1,2]. 4. Using implicit differentiation, find 2: if sin(2x 7y) = 16y. 5. Let f be a function whose graph is pictured below, and let F(x) = fif(t)dt. (3) Find F(1) and F(3). (b) Find the intervals on which F is increasing or decreasing