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Calculus
Show that for two scalar fields f and g:
∆× ( f∆g)+∆×( g∆f)=0
∆× ( f∆g)+∆×( g∆f)=0
Calculus
Determine whether the following vector field is solenoidal, irrotational or both
F= x^2.yi + xyzj - x^2.y^2.k
F= x^2.yi + xyzj - x^2.y^2.k
Calculus
A jogger runs from her home to a point A, which is 6 km away. For there 6 km, she
begins by running at a constant speed till she reaches a hilly portion 2 km from her
home. Here her speed slows down while she runs up the hill, which is a 1-km run.
Then she speeds up while running down the hill. The last 2 km of the run are again at
constant speed. Draw a graph to show the jogger’s speed as a function of the distance
from her home. Also find the range of this function.
begins by running at a constant speed till she reaches a hilly portion 2 km from her
home. Here her speed slows down while she runs up the hill, which is a 1-km run.
Then she speeds up while running down the hill. The last 2 km of the run are again at
constant speed. Draw a graph to show the jogger’s speed as a function of the distance
from her home. Also find the range of this function.
Calculus
The original function used to model the cost of producing x PortaBoys Game Systems was
C(x) = 80x + 150.
While developing their newest game, Sasquatch Attack!, the makers of the PortaBoy revised their cost function using a cubic polynomial. The new cost of producing x PortaBoys is given by
C(x) = .03x3 − 4.5x2 + 221x + 250.
Market research indicates that the demand function
p(x) = −1.5x + 250
remains unchanged. Find the production level x that maximizes the profit made by producing and selling x PortaBoys. (Round your answer to the nearest whole number.)
C(x) = 80x + 150.
While developing their newest game, Sasquatch Attack!, the makers of the PortaBoy revised their cost function using a cubic polynomial. The new cost of producing x PortaBoys is given by
C(x) = .03x3 − 4.5x2 + 221x + 250.
Market research indicates that the demand function
p(x) = −1.5x + 250
remains unchanged. Find the production level x that maximizes the profit made by producing and selling x PortaBoys. (Round your answer to the nearest whole number.)
Calculus
Using Stokes' Theorem evaluate the line integral integrate at C F.dI where F= you+ xz^3 .j - zy^3 .k andC is circle x^2+.y^2=5 in the plane and=-3.
Calculus
Using Green's Theorem evaluate the integral of area enclosed by at C(y^2 .dx +3 xydy) where C is a semi circle of radius 1 in the upper half plane, centered at origin.
Calculus
Determine the direction in which the scalar field f(x,y)= xy^2 + x^3. y increase the fastest at the point (1, 2).
Calculus
Calculate the work done by a force F=2xi+3yj in moving a particle once counterclockwise along the ellipse x^2/4 + y^2/9 =1 .what do you understand from the answer,?
Calculus
A jogger runs from her home to a point A, which is 6 km away. For there 6 km, she
begins by running at a constant speed till she reaches a hilly portion 2 km from her
home. Here her speed slows down while she runs up the hill, which is a 1-km run.
Then she speeds up while running down the hill. The last 2 km of the run are again at
constant speed. Draw a graph to show the jogger’s speed as a function of the distance
from her home. Also find the range of this function.
begins by running at a constant speed till she reaches a hilly portion 2 km from her
home. Here her speed slows down while she runs up the hill, which is a 1-km run.
Then she speeds up while running down the hill. The last 2 km of the run are again at
constant speed. Draw a graph to show the jogger’s speed as a function of the distance
from her home. Also find the range of this function.
Calculus
Find the volume of the solid obtained by revolving the curve x= a coscubetheta ,y =a sincubetheta about the y-axis.
