Calculus Answers

A comparison between the Darboux-integral and the Riemann-integral.

A comparison between the Darboux-integral and the Riemann-integral.

A comparison between the Darboux-integral and the Riemann-integral.

Let Ω be the region above y+z= 2, below z= 4, and between x= 0 and x= 4−y^2 a triple integral for the volume of the region. Set up an integral to represent the volume of Ω in all six orders and then fully solve ONE of them.

Evaluate an appropriate double integral (in Cartesian coordinates) to find the area of the ellipse x^2/a^2+y^2/b^2 = 1, a, b >0 What happens to your answer in the limit a→0^+? Does this make sense?

Prove that the function f(x, y) = |xy| / xy is integrable on R= [−1,1]×[−1,1].

Qdx = 250 + 0.65I – 0.2Px2 + 0.5PxPy + 0.21Ax

Where
I = $250
Px= 7
Py = 4
Ax = 20
Determine
a) Price elasticity of demand for commodity x and interprete your result
b) Cross elasticity of demand for commodity x and y and interprete your result
c) Income elasticity of demand for commodity x and interprete your result
d) Advertisement elasticity of commodity x and interprete your result

1. A drum of oil in the shape of a cone is leaking oil at a constant rate of . The base radius of the drum is 7 cm and the height of the drum is 15 cm.
1.1 At what rate is the depth of oil in the drum changing when the depth of oil is 5 cm?

Let a and β be multi-indices such that β ≤ a. Prove that ∂^(β) x^(a) = (a,β) β!x^(a - β) if β≤a

Use Green’s theorem to evaluate ∫ (x^5+2y)dx + (4x-6y^3)dy where C is the circle x^2 + y ^2 = 4 .