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Graph and discuss the continuity of the following functions:
1.f(x)= 3x-1, x≠1
2.f(x)=1/x+1
a right circular cylinder has a fixed height of 6 units. Find the rate of change of its volume V with respect to the radius r of its base. Find the rate of change of the total surface area A with respect to r.
. Find an equation of the tangent plane to the surface at the given point. f(x, y) = x2 − 2xy + y2, (1, 5, 16) with maple lab please
Find the average value of f (x, y) over the region R f(x, y) = ex + y R: triangle with vertices (0, 0), (0, 3), (3, 3) with maple lab please
Find the average value of f (x, y) over the region R f(x, y) = ex + y R: triangle with vertices (0, 0), (0, 3), (3, 3) with maple lab
You are newly hired in a soft drink making compan They want to introduce 400ml and one liter tin packs for
the promotion of their brand. For making these tin packs the cost of the top and bottom of a tin is 5/3
times the cost of the body/cylinder. The company assign you to suggest the dimensions of the required
tin packs which also minimize the cost of production of the tin packs. Moreover, check whether there
are more options or is only one option to construct the required tin packs to get optimize solution.
Furthermore, the total budget for this new brand was assigned only $1 million. Therefore, also find how
many tin packs of two sizes must be prepared to get the maximum profit if there is profit on each tin of
400ml is one dollar and $3 for each tin pack of one liter.
which will provide you the optimal dimensions subject to the constraint of cost. The program will take
dimensions of the tin packs as input and return the cost and quantity of each size.
x=e^t, y=sint, z=x^2+xy
dz/dt = ???
Determine and sketech the set of pairs (x, y) in R×R that satisfy: i)|x|=|y| ii)|x|-|y|=2
Find these terms of the sequence {an}, where an =
2 · (−3)n + 5n.
a) a0
b) a1
c) a4
d) a5
(a) Evaluate∫[
x
√x
2+1
]dx.
(b) Use MATLAB to generate some typical integral curves of f(x) =
x
√x
2+1
over the
interval (−5,5).
