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Show that line integral is independent of path by finding a potential function for F
F(x,y) = (sin x − x sin y) j + (cos y + y cos x) i
Explain when it is necessary to convert a double integral from cartesian coordinates to
polar coordinates.
A closed rectangular box with a volume of 16 ft cube is to be made of three different materials. The cost of the material for the top and the bottom is $9 per sq. ft, the cost of the material for the front and the back is $8 per sq. ft. and the cost of the material for other two sides is $6 per sq. ft. Find the dimensions of the box (by two ways if possible) so that the cost of materials is minimized.
Find volume of region (by more than one different way if possible) that is bounded by graphs of equations:
y^2+x^2=z, 4z=24-2x^2-2y^2
Give the definition of series and explain in your own words what is a convergent and divergent series. Would it be possible to have a series that is not convergent nor divergent? You need to provide an example for each of the qualitatively different cases.
F(x)=35x^4+15x^30x^2-15x+3
Differentiate the following with regard to x
y=ln( square toot X multiple e^x^2)
Determine the following integral
∫_0^(π/2)▒〖sin2x cosx dx〗
lim┬(n→∞)〖(x^3+5)/(〖2x〗^4-1)〗
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
