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DM. Let a and b be two cardinal numbers. Modify Cantor’s definition of a < b to define a ≤ b. (Hint: Examine what happens if you drop condition (a) from Cantor’s definition of a < b.) 2. Prove that a ≤ a. 3. Prove that if a ≤ b and b ≤ c, then a ≤ c. 4. Do you think that a ≤ b and b ≤ a imply
a = b? Explain your reasoning. (Hint: This is not as trivial as it might look.)
Find the area enclosed by the curve r = 5cosθ
Find the volume of the solid generated by revolving the region bounded by the curves about the y axis y=x^3 , x=0 , y=1
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1. The volume of a sphere is increasing at the rate of 6 cm^3/hr. at what rate is the surface area increasing when the radius is 50cm?
2. a plane 3000ft from the earth's surface is flying east at the rate of 120mph. it passes directly over a car also going east at 60mph. how fast are they separating when the distance between them is 5000ft
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1. water flows into a conical vessel 18cm deep and 10cm in a diameter. if the rate at which the water surface is rising is 27.52mm/s, how fast is the water flowing into the conical vesel in m^3/s when the initial depth of water is 12cm?
1. the sum of two numbers is 12. find the minimum value of the sum of their cubes.
2. a triangular corner lot has perpendicular sides of lengths 120m and 160m, resectively.
a. find the area of the longest rectangular building that can be constructed on the lot with sides parallel to the street.
b. find the perimeter that closes the building.
c. if it costs P6,000.00 per square meter of floor area of the building. how much would be the approximate cost if a three-storey building is to be constructes.
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1. if y= ax^3 + bx^2 and its point of inflection is at (2,8), what are the values of a and b?
2. graph the curve and find the point of inflection: y= (9x^2 - x^3 + 6)/ (6).
3. graph the curve and find the point of inflection: y= x^3 - 3x^2 + 6.
differentiate implicity the following equations. show complete solutions
1. e^(2x+3y) =x^2 - In(xy^3)
2. x^2 y^3 = xy+x^3 + y^2 + 5
determine the critical points of f(x)=8x3+81x2-42x-8
1. Determine the critical points of each of
