Please solve and explain all steps.For 7d, please select the right option to complete the answer.

(c) Find any horizontal and vertical asymptotes of f. . . . Horizontal asymptotes y = Vertical asymptotes x = N/A even, odd, neither ff-x) = f(x) or f(-x) = -f(x) (incorrect) (d) The function f is because for all x in the domain 5. (1 point) of f, and therefore its graph is symmetric about the 2 Find the limit. Use l' Hospital's Rule if appropriate. Use INF to represent positive infinity, NINF for negative infinity, and D xaxis , yaxis origin line yEx not applicable for the limit does not exist. (e) Sketch a graph of the function f without having a graph- 3 Cosx lim ing calculator do it for you. Plot the y-intercept and the x- x-+(n/2)+ 1 - sinx intercepts, if they are known. Draw dashed lines for horizon- Answer(s) submitted: tal and vertical asymptotes. Plot the points where f has local . ninf maxima, local minima, and inflection points. Use what you (correct) know from parts (a) and (b) to sketch the remaining parts of 6. (1 point) the graph of f. Use any symmetry from part (d) to your advan- he limit. Use l'Hospital's Rule if appropriate. Use INF tage. Sketching graphs is an important skill that takes practice, to represent positive infinity, NINF for negative infinity, and D and you may be asked to do it on quizzes or exams. for the limit does not exist. Answer(s) submitted: lim Ix + Isinx x-+0 2x + 2cosx Answer(s) submitted: (correct) . . . . 7. (1 point) Please answer the following questions about the function f (x) = (12+10)(1-x2). Instructions: If you are asked to find x- or y-values, enter either (incorrect) a number, a list of numbers separated by commas, or None if there aren't any solutions. Use interval notation if you are 8. (1 point) A rectangle is inscribed with its base on the x- asked to find an interval or union of intervals, and enter { } if axis and its upper corners on the parabola y = 4- x-. What the interval is empty. are the dimensions of such a rectangle with the greatest possible area? Width = (a) Find the critical numbers of f, where it is increasing and Height = decreasing, and its local extrema. Answer(s) submitted: Critical numbers x . (4sqrt3) /3 Increasing on the interval . 8/3 Decreasing on the interval (correct) Local maxima x = 9. (1 point) A cylinder is inscribed in a right circular cone Local minima x = of height 4.5 and radius (at the base) equal to 4.5. What are the dimensions of such a cylinder which has maximum volume? Radius = Height = (b) Find where f is concave up, concave down, and has in- Answer(s) submitted: flection points. Concave up on the interval Concave down on the interval (incorrect) Inflection points x =