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If money is deposited into an account at a continuous rate of 2000 shillings per year, and account earns 8% compounded continuously. Find the amount in the account at any time t and the amount in the account after 5 years if initially the account had 10,000 shillings.
A tank having a capacity of 1000 liters, initially contains 400 liters of sugar water having a concen-
tration of 0.2 Kg of sugar for each liter of water. At time zero, sugar water with a concentration of
50 gm of sugar per liter begins pumped into the tank at a rate of 2 liter per minute. Simultaneously,
a drain is opened at the bottom of the tank so that the volume of the sugar-water solution in the
tank reduces 1 liter per minute. Determine the following:
a) find and classify the critical points of the functions f(x) = 2x^3 + 3x^2 - 12 x +1 into maximum, minimum and inflection points as appreciate.
(b) The sum of two positive numbers is S. find the maximum value of their product.
Determine whether the vectors are linearly dependent or independent (1,2,1),(-1,0,1) and (2,-1,4)
Using taylor series expansion obtain a power series solution to the initial value problem
(2x2-3)d2y/dx2-2xdy/dx+y=0 y(0)=1 y'(0)=7
Determine the general solution to the exact differential equation
(e2y-ycosxy)dx+(2xe2y-xcosxy+2y)dy=0
Solve the equation dy/dx= -(x2+y2)/xy
Find the general solution of the equation d2y/dx2+4dy/dx+4y=4e-2x
Determine the differential equation arising from y=c1e5x+c2e7x
