Assignment9: Problem 2 (1 point) Evaluate the indicated limit. Enter INF for co, -INF for -oo, or DNE if the limit does not exist, but is neither oo nor -CO. oc 3 + 9ac2 - 3x + 8 lim help (numbers) 20- - 00 3 - 5x2Assignment9: Problem 3 (1 point) Identify the horizontal and vertical asymptotes, if any, of the given function. f ( ac ) = 9ac2 + 27x + 18 5x2 + 5x - 10 Separate multiple answers by commas. Enter DNE if an asymptote does not exist. a. Horizontal asymptote(s): y = help (numbers) b. Vertical asymptote(s): x =In the following questions, consider the function f(:z:) = 4.53:2 :33 + 1233 + 3.5. Enter DNE if an answer does not exist. 1. Determine the domain of f (as an interval) D help (intervals) 2. Find the critical values of f. C] (Separate multiple answers with commas.) 3. List the :vvalues of any possible points of inflection of f. U (Separate multiple answers with commas.) 4. Find the vertical asymptotes. a: 2:] (Separate multiple answers with commas.) 5. Find the horizontal aymptotes. y :C] (Separate multiple answers with commas.) 6. Use a number line analysis to complete the following (enter answers as intervals). f is increasing on: f is decreasing on: f is concave up on: f is concave down on: D 7. Evaluate f at each critical point and possible point of inflection. List all such points below. Each point should be entered as an ordered pair (that is, in the form (:13, y)). D (Separate multiple answers with commas.) Assignment9: Problem 5 (1 point) Find the minimum sum of two positive numbers (not necessarily integers) whose product is 825. C] help (numbers) Assignment9: Problem 6 (1 point) A rancher has 288 feet of fencing with which to construct adjacent, equally sized rectangular pens as shown in the figure above. What dimensions should these pens have to maximize the enclosed area? :1: 2 ft help (numbers) y : ft Maximum area S =8 132 AssignmentQ: Problem 7 (1 point) The Ettinsmoor Postal Service charges more for boxes whose combined length and girth exceeds 342 mm. The length of a package is the length 6 of its longest side; the girth is the perimeter of the cross section, 221) | 2b,. What is the maximum volume of a package with a square cross section (21) : h ) that does not exceed the 342 mm standard? Maximum volume V = C] mm3 help (numbers) Assignment9: Problem 8 (1 point) offshore facilityr . power. x . plant A power line is to be run to an offshore facility as shown in the figure above. The offshore facility is D = 1 mile at sea and L = 11 miles along the shoreline from the power plant. It costs $ 45,000 per mile to lay a power line underground and $ 90,000 per mile to run the line underwater. How much of the power line should be run underground, and how much underwater to minimize the overall costs? Length underground (in miles): help (numbers) Length underwater (in miles): Minimal cost (in dollars): C]