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A silo consists of a right circular cylinder surmounted by a right circular
cone cover. What is the maximum volume of this silo that can be
constructed using a 100 m2
of plane GI sheet ?
8: Convergence of summation (n!(n+1)!)/(3n)!
9: Radius of convergence of summation n=0 to infinity (n^3)x^3n/n^4+1
1:Examine the series for convergence for summation of ((-1)^(n-1) sin(nx))/n^3
2: Test for convergence of summation (x^n)/(2n)!
3: Examine the following series for absolute convergence of x-(x^2/2)+(x^3/3)-(x^4/4)+......
4:Test convergence of series
1+(1*2^2)/(1*3*5)+(1*2^2*3^2)
5: Test convergence of summation (x^n)/n!
6:Examine the following series for absolute convergence of 1+(x/2)+(x^2/3^2)+(x^3/4^3)+......(x>0)
7: Examine convergence of summation 1/root n
A 2 kg mass is attached to a spring having spring constant 10 N/m. The mass is placed in a surrounding medium with damping force numerically equal to 8 times the instantaneous velocity. The mass is initially released from rest at 1 meter above the equilibrium position. Find the equation of motion.
A steel storage tank for propane gas is to be constructed in the shape
of a right circular cylinder with a hemisphere at both ends. If the
desired capacity is 100 cu. ft., what dimensions will require the least
amount of steel ?
Find the dimensions of the rectangle of maximum area having two
vertices on the x-axis and 2 vertices above the x-axis on the graph of y
= 4 – x2
Find the value of C in the rolle's theorem, where f(x) =cos x and (-pie/2)<C<(pie/2).
f(x,y)=x²-xy+y²/2+3
Lim ( y 3 – y 2 – y -2 )
y – 2 2y 3 – 5y 2 + 5y – 6
Derive a formula for
n
∑
i= i3 a telescoping sum with terms f(I) = i4
