Question For this problem, consider the function, f (x) = ln (x^2 + 6x + 10)  a) Find all the critical numbers of f(x). (b) Determine the intervals over which the function is increasing/decreasing. (c) Classify each critical point as a local maximum/local minimum. (d) Determine the intervals over which the function is concave up/concave down. (e) Find all the inflection points of f(x).

(1 point) You are given the polar curve r = 3 cos(O). (a) List all of the points (r, 0) where the tangent line is horizontal. In entering your answer, list the points starting with the smallest value of r and limit yourself to r> 0 and 0 <o<27. If two or more points share the same value of r, list those starting with the smallest value of 0. If any blanks are unused, type an upper-case "N" in them. Point 1: (r,0) =( Point 2: (r,) =( Point 3: (r, 0) = (b) List all of the points (r, 0) where the tangent line is vertical. In entering your answer, list the points starting with the smallest value of r and limit yourself to r> 0 and 0 <O<21. If two or more points share the same value of r, list those starting with the smallest value of 0. If any blanks are unused, type an upper-case "N" in them. Point 1: (r, 4) = Point 2: (r, 8) = Point 3: (r, 8) =

8.F Unanswered. 3 attempts left Figure shows solid disk with initial (without a hole yet) mass 5.0 kg and radius R= 0.2 m with a circular hole of radius R/2. Find moment of inertia of this figure relatively the center of initial disk. Type your response Submit 8.F Unanswered. 3 attempts left Figure shows solid disk with initial (without a hole yet) mass 5.0 kg and radius R= 0.2 m with a circular hole of radius R/2. Find moment of inertia of this figure relatively the center of initial disk. Type your response Submit

(1 point) Find a formula for Sn, n > 1, if Sn is given by 8 4 5 6 7 6' 10' 14'18 22 Sn =

Find an equation for the rational function in the given graph. 10 an -10 -5 TTT 5 10 5 -10 The equation of the graph is f(x) = (Simplify your answer.)

(i) Express rectangular coordinates in terms of cylindrical coordinates (ii) Consider the solid G bounded by the surfaces x2 + y2 4 and x2 + y2 = 9, above by the surface z = 13 – x2 - y², and below by the surface z = 0. = = - (a) What are the surfaces x2 + y2 = 4 and x2 + y2 = 9? + (b) What is the surface z = 13 x² - y²? (c) What is the surface z = 0? Sketch the part of the boundary of the solid G which belongs to the surface z = 0. (d) Use triple integral to compute the volume V of the solid G. (e) Use triple integral to find the mass M of the solid G if its density is 8(x, y, z) = e12–22-y2–2.

Find an equation for the rational function in the given graph. 10 5 %3D -10 -5 10 -5 -10 The equation of the graph is f(x) = . (Simplify your answer.) %3D 5. 10 5- -10 -5 5. 10 -5 -10 OK