Many and more students who study any branch in mathematics face a lot of troubles. And calculus is one of these problems. Trying hard to learn all the formulas the students finish up with a huge number of calculus questions that cause many problems in the studying process. We have worked out our service system so that you could get the calculus answers any time you need them with a minimum waste of time. If you have nobody to help you with the calculus problems – we are at your disposal!

Calculus

Find the area included between the curve x^3 + y^3 = 3axy and its asymptote

Calculus

Find a third degree McLaurin expansion of f (x) =sec2x

Calculus

∫(x)= tanax dx

Calculus

∫ (x) = sin 2x

Calculus

Johnny is designing a rectangular poster to contain 24in^2 of printing with a 3-in margin at the top and bottom and a 2-in margin at each side. what overall dimensions will minimize the amount of paper used?

Calculus

A fence must be built to enclose a rectangular area of 45,000ft^2. Fencing material cost $1 per foot for the two sides facing north and south and $2 per foot for the other two sides. Find the cost of the least expensive fence.

Calculus

A right triangular plate of base 3.0 m and height 1.5 m is submerged vertically in water, with top
vertex 3.5 m below the surface. Find the force on one side of the plate.

Calculus

Find the force on one side of a cubical container 6.0 cm on an edge if the container is filled with
mercury. The weight density of mercury is 250 kN/m³.

Calculus

HardyWeinberg equilibrium problem
if the three genotypes AA, Aa, and aa have respective frequencies pAA =θ^2, pAa = 2θ(1 − θ), and paa = (1 − θ)^2,
n! / (divide) n1! n2! n3! PAA^n1 PAa^n2 Paa^n3
where n = n1 + n2 + n3. This probablity depends on θ.
There is a method called the maximum likelihood method, that can be used to estimate θ. The principle
is simple: We find the value of θ that maximizes the probability of the observed data. Since the coefficient n! / (divide) n1! n2! n3!
does not depend on θ, we need only maximize
L(θ) = PAA^n1 PAa^n2 Paa^n3
(a) Show that if L(θ) is maximal for θ = ˆθ then ln(L(θ)) is maximal for θ = ˆθ.
(Note that L is strictly positive and twice differentiable.)
(b) Use the result in (a) to find the value ˆθ that maximizes L(θ)

Calculus

Which of the following statements are true? Give reasons for your answers, in the
form of a short proof or a counterexample.
i)
2
2
2
dx
dy
dx
d y
=
ii) The inverse function of 3x
y = e is ln x
3
1
y = .
iii) If f is increasing and 0 )x(f > on an interval I, then
)x(f
1
)x(g = is decreasing on I.
iv) An equation of the tangent line to the parabola 2
y = x at )4,2 (− is
y − 4 = 2 x(x + )2 .
v) If f is one-one onto and differentiable on R , then
f )6(
1
f( )6()'
1
′
=
−
.