(1) Determine the uniform convergence of the following sequences of functions: xn 2+nan-1 fn(2) = x = [0, 2]; 9n(x) = e¯ " sin (x + JM); xER.

Let f(x) = 2³ – 18x2 – 240x. Complete this problem without a graphing calculator. (a) The derivative of f(x) is f'(x) = (b) As a comma-separated list, the critical points of f are x = Since f is continuous on the closed interval [-5, 18], f has both an absolute maximum and an absolute minimum on the interval [-5, 18] according to the Extreme Value Theorem. To find the extreme values, we evaluate f at the endpoints and at the critical points. (c) As a comma-separated list, the y-values corresponding to the critical points and endpoints are y = (d) The minimum value of f on [-5, 18] is y = the minimum value occurs at x = and this x is a(n) ? (e) The maximum value of f on [-5, 18] is y = the maximum value occurs at = and this x is a(n) ?

Let f(x) = |3 – x²|] Estimate f'(1)d (Hint: h = 0.0001)

x²- 2x-8 if x+4 (4) F (x)=, х-4 • if f is continuous at x=4, а, if x = 4 then a =.