Find the power series solution for the equation y'' + (sinx)y =
x; y(0) = 0; y'(0) = 1
Provide the recurrence relation for the coefficients and derive
at least 3 non-zero terms of the solution.
a)
Find the value of the Wronskian of the functions f =
x^7
and g = x^8 at the piont x = 1.
b)
Let y be the solution of the equation y ″ − 5 y ′ + 6
y = 0
satisfying the conditions y ( 0 ) = 1 and y ′ ( 0 ) = 2.
Find ln ( y ( 1 ) ).
c)
Let y be the solution of the equation y ″ + 2 y ′...
given the function y=x+cosx on the interval [0,2pi] find the
intervals of increasing and decreasing, local or absolute
extrema(s), the intervals of concavity and the inflection points.
use the information to sketch the graph of y=x+cosx on the interval
[0,2pi]
For f(x)= cos2x + sinx, find the intervals where the
function is increasing, decreasing, relative extrema, concavity,
and points of inflection on the interval [0,2π)
Find the volume of the solid obtained by revolving the area
under y=cosx on [0,π/2] around the y-axis.
The total weight of a cable hanging from the ceiling plus the
bucket of coal it is attached to is F(x)=1800−2x pounds when the
bucket is xx feet off the ground (the cable gets shorter as the
bucket is lifted, so the weight decreases). Find the total work
done in lifting the bucket from the ground to 100 feet off the
ground.