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Category > Calculus Posted 09 Jul 2017 My Price 6.00

Limits at infinity

1. Limits at infinity
a. Lim (x – inf) ((8-4x^2+3x^3-x)/ (2-x^3)
This is a fraction. (8-4x^2+3x^3-x) = Numerator
(2-x)^3 = Denominator
b. Lim (x – Inf) (Sqrt(4x^4+2)/(3x^2+5)
This is a fraction. (Sqrt(4x^4+2)=Numerator
(3x^2+5)=Denominator
2. Text Optimizations
a. A farmer is creating a rectangular pen for his animals that is adjacent to a barn. (Note: no fencing is needed for that side). He has 180 feet of fencing to use. What length and width would produce the largest area for the pen? What is the area of the pen? Let L represent length, w represent width and A represent area.
3.
b. A can of soup is being constructed out of aluminum. The volume of the can is 24 cubic inches. What height should be the height of the can in order to minimize the amount of aluminum used? Let h be the height of the cylinder and r be the radius of the top and bottom circle. c. The sum of two nonnegative numbers is 100. What is the maximum value of the product of these two numbers? d. A rectangular swimming pool is to be built with an area of 1800 square feet. The owner wants 5­foot­wide decks along either side and 10­foot­wide decks at the two ends. Find the dimensions of the smallest piece of property on which the pool can be
built satisfying these conditions. (See Illustration below).

Answers

SuperTutor
(15)
Status NEW Posted 09 Jul 2017 11:07 PM My Price 6.00

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