Consider the twice-differentiable function f(x) with selected values in the table, the composite function p(x), and the piecewise-defined function w(x) for x 2 0 given below. p(x) =Vf ( 2x+ 1) + 5x w(x) (3,5) x f(x) f(x) (0, 5) 3 8 -6 (3,2) 1.4 9 -1 10 12 a) Find the slope of the line tangent to p(x) at x = 3. Show your process. 3 b) Evaluate ! (xf (x-) + 6) dx show the work that leads to your answer. c) Find the area between w(x) and the x-axis for x 2 0. Show the work that leads to your answer. d) Consider the series below related to w(x) above and determine if it converges or diverges. Justify. w(n) e) Setup an expression that would find the volume of the solid if the region bounded by w(x) for 4 s x s 10 and the x-axis were revolved around the line y = -2. Do not solve. ) Give the second degree Taylor Polynomial centered at t = 6 for R(t) shown below. 2. 7,

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Cylinders

A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.

Cones

A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.