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Find the volume in the first octant bounded by x+y+z=9, and the inside cylinder 3y=27-x^3
Give an example of a function of two variables such thatf(0,0) = 0 butfis NOT continuousat (0,0). Explain why the functionfis NOT continuous at (0,0).
Give an example of a function of two variables such that f(0,0) = 0 but f is NOT continuous at (0,0). Explain why the function f is NOT continuous at (0,0).
A Manufacturer produces two products, the Klunk and the Klick. Klunk has a contribution
to profit of $3, and the Klick $4 per unit. The manufacturer wishes to establish the weekly
production plan that maximizes profit. Production of these products is limited to machine,
labor and material constraints. Each Klunk requires four hours machining, four hours labor
and one kilogram of material, where as each Klick requires two hours machining, six hours
labor and one kilogram of material. Machining and labor has a maximum of one hundred
and one hundred and eighty hours available, and total material available is forty kilograms.
Because of a trade agreement, sales of Klunk are limited to a weekly maximum of twenty
units and to honor an agreement with an old established customer at least ten units of Klick
must be sold each week.
i. Determine graphically using linear programming a suitable production mix of Klunk
and Klick. [12]
ii. What will be the company’s maximum profit?
Determine the length of the curve 𝑥 = 𝑦^2 /2 for 0 ≤ 𝑥 ≤ 1/2 . Assume 𝑦 positive.
The functions f and g are defined by f(x) =1/(1-3x) and g(x) =log1/3(3x-2)-log3(x) respectively
1. Write down the sets Df (ehe domain of f) and Dg (the domain of g)
2. Solve the inequality f(x) > 2 for x"\\isin" Df
3. Solve the inequality f(x) ≥ 2 for x"\\isin" Dg
Hint: Use the change of base formula
2. The formula h(t) = -16t² + 32t + 80 gives the height b above the ground, in feet (ft), of an object thrown, at t = 0, straight upward from the top of an 80 ft building. What is the highest point reached by the object? How long does it take the object to reach its highest point?
1. The profit of a company is given by P(x) = 5 000 +1 000x-5x² where x is the amount (in thousands of pesos) that the company spends on advertising.
a. Find the amount x that the company has to spend to maximize its profit.
b. Find the maximum profit.
Can You Show Me the Way? Complete the table of values of the exponential function. Then, draw its graph in the given coordinate plane. 2 3 1 х -3 -2 -1 0 f(x) = 3*1. How will you describe the graph? 2. In which quadrant/s do the graph occupies?3. What are the other possible values of x? Describe the range of the possible values of x? 4.What do you think now is the range of the function? 5. What other observations can you give?
2. Use change of variables technique to integrate the following
Z
x(3x − 2) 1
2 dx
