Question If f(x, y) = 49 – 7x2 - y2, find f{(1, 6) and fy(1, 6). Illustrate with either hand drawn sketches or computer plots. (1, 6) = fy(1,6) =

(1 point) if the gradient of /is Vf=x+] - 3y + 4zxk and the point P = (8.--8, 10) lies on the level surface f(x, y, z) = 0, find an equation for the tangent plane to the surface at the point P. SHE

For the following exercises, find the lengths of the functions of y over the given interval. If you cannot evaluate the integral exactly, use technology to approximate it. 181. y = 5 - 3x from y = 0 to y = 4 – 4

C. Which of the following organisms are most closely related? Are any two the same species? On what did you base your answer? 2.0 A B D C Rod Rod Coccus Rod + + Fermentative Oxidative Fermentative Fermentative Characteristics Morphology Gram Reaction Glucose utilization Cytochrome oxidase GC moles % Present Present Absent Absent 48-52 23-40 50-54 49-53

For this week's discussion, you are asked to generate a continuous and differentiable function f (2) with the following properties: • f(x) is decreasing at x = -6 • f(x) has a local minimum at x = -3 • f (x) has a local maximum at x = 3 Hints: • Use calculus! • Before specifying a function f (2), first determine requirements for its derivative f' (2). For example, one of the requirements is that f' (-3) = 0. • If you want to find a function g(x) such that g(-9) = 0 and g(8) = 0, then you could try g(x) = (x + 9) (x – 8). • If you have a possible function for f' (2), then use the techniques in Indefinite Integrals this Module to try a possible f (x). You can generate a plot of your function by clicking the plotting option (the page option with a "P" next to your function input). You may want to do this before clicking "How Did I Do?". Notice that the label "f(2) =" is already provided for you. Once you are ready to check your function, click "How Did I Do?" below (unlimited attempts). Please note that the bounds on the x-axis go from -6 to 6. f(x) = How Did I Do? Try Another

. Explain which types of market inefficiencies derive from monopolies. Use examples from the textbook to support your claims. • Describe the types of inefficiencies that derive from monopolistic competition. Use examples from the textbook to support your claims. How are monopolies and monopolistic competitive firms profitable? Use examples from the textbook . Explain which types of market inefficiencies derive from monopolies. Use examples from the textbook to support your claims. • Describe the types of inefficiencies that derive from monopolistic competition. Use examples from the textbook to support your claims. How are monopolies and monopolistic competitive firms profitable? Use examples from the textbook to support your analysis.

CLEARLY PLEASE Toluene is produced by hydroforming conversion of n-heptane in a Cr203@-A1203 catalyst medium. The operating conditions of the process are given on the flow chart. The solvent used in the process is recovered. CH3CH2CH2CH2CH2CH2CH2 - CH3CH3 + 4H2 Toluene production efficiency is 15% based on n-heptane fed into the process. The solvent ratio used in the extractor is 10 kg solvent / 1 kg toluene. According to this, a. Calculate how much heat must be added or removed to keep the reactor isothermal at 425 °C. b. What is the temperature of the n-heptane or solvent stream leaving the extractor. (The temperatures of the n- heptane and solvent streams can be considered the same.) но | 425 °C Cooler n-Heptane Superheater 425 °C 18°C 18 °C Catalytic Reactor HO Saturated Toluene vapour n-Heptane . 38c Solvent Heat Heat Extractor Still Exchanger Separator 18 °C 120 °C Solvent Solvent+Toluene