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Find a solution u(x,t) to the problem šš¢ šš” = 1.71 š^2š¢/šš„^2 , š¢(š„, 0) = š šš ( šš„/2 ) + 3 š šš ( 5šš„/2 ) , 0 < š„ < 2
Evaluate
lim 3nĪ£r=1 n^2/(4n+r)^3
nāā
Determine whether the function f (x) = x ā x1 is odd, even or neither.
Find the unit normal to the surface š¦ = š„ + š§ 3 at the point (1,2,1).Ā
A manufacturer knows that if x goods are demanded on a particular week, the total cost and revenue functions will be:š¶(š„) = 14 + 3š„ ššš š (š„) = 18š„ ā 2š„ 2 respectively.
i. Calculate the level of demand that will maximize profits (6 marks)
ii. Calculate the amount of profit that will be realized at this maximum point. (4 marks)Ā
The quantity demanded per month of a product is 250 units when the unit price is Ksh 1400. The quantity demanded per month of the same product is 1000 when the unit price is Ksh 1100. The quantity suppliers will supply to the market is 750 units when the unit price is Ksh 600 or lower and will supply 2250 units if the price is Ksh 800. Both the Supply and Demand functions are known to be linear. Required
: i. Find the demand function (2 marks)
ii.Find the supply function (2 marks)
iii. find the equilibrium price and quantity (4 marks)
if the total cost of producing x liters of salad oil is C(x)=0.375x^3-0.99x^2-200x+60,000
find the marginal cost at an output of 100litres
A Norman window consists of rectangle surmounted by a semicircle. If the
perimeter of a Norman window is 32 ft, what should be the radius of the
semicircle and the height of the rectangle such that the window will admit most
light?
. A model that describes the population p(t ) of a fishery in which harvesting takes place at
a constant rate is given by
dp/dt=kp-h
where k and h are positive constants.
(a) Solve the DE subject to P(0) = p
(b) Describe the behavior of the population P(t) for increasing time in the three cases for p=h/k , p=h/k , and 0<p<h/k
(c) Use the results from part (b) to determine whether the fish population will ever go extinct
in finite time, that is, whether there exists a time T>0 such that p(t )=0 . If the population
goes extinct, then find T
If x(t+y) = t^2 + y^2. Show that (partial x/partial t - partial x/partial y)^2 = 4[1 - partial x/partial t - partial x/partial y]
