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d²y/dx²-6dy/dx+9y=x²e^(3x)
Verify rolle's theorem
f(x)=(x-a)^m(x-b)^n,where m,n are positive intigers, in the interval [a,b]
A string is stretched and fastened to two points at a distance 0
l
0 apart. Motion is started by
displacing the string in the form y = k sin πx
l
from which it is released at time t = 0. Show
that the displacement of any point on the string at a distance x from one end at time t is
given by k sin πx
l
cos πax
l
Differentiate the following with regard to x :
y=x^4sinx
Determine the area enclosed by y =x and
y =x^2
Differentiate the following with regard to x
y=2x-8/5-3x^2
A cobb douglas production function for a new company is given by F(x,y)=50x3/5y2/5. Where x represents the units of labor and y represents the units of capital. Suppose the units of labor and the capital cost is $200 and $100 each respectively and the budget constraint is $30,000. Find the maximum production level for this manufacturer.
The marginal revenue of a company is given by MR-40 +60 +
602, where Q is the number of units sold for a period. Find the total revenue
function if at Q-0 total revenue is equal to 0.
The temperature T( ◦C) in Antalya is found to be changing at a rate given by T 0 (t) = −0.02(t − 7)(t − 14) ◦C/hour at t hours past midnight. By how much does the temperature change between 8 A.M. and 8 P.M.? (Use calculus to nd the approximate value.)
A geometric progression has first term and common ratio
i) Find the set of values of x for which geometric progression has a sum to infinity.
- ii) Find the value of x for which the sum to infinity of geometric progression
