Search & Filtering
- D2((x+1)2/x-1) ans, 8/(x-1)3
- D(ln(x2-2x+1)) ans, 2/x-1
- D(x2+2x-3) ans, 2x+2
- D2(xe3x-e4x) ans, 9xe3x+633x-16e4x
Use Monte Carlo integration to estimate the integral of a function. Also calculate the error-> limit(1,0) ∫ 𝑥 ^2 (3𝑥 + 1)𝑑x
Evaluate the following functions in differential operator form.
- D2((x+1)2/x-1) Answer: 8/(x-1)3
- D(ln(x2+2x+1) Answer: 2/x-1
A manufacturer packages his product in a 500-ml cylindrical can. The material for the
top costs four times as much per square centimeter as that to be used for the bottom and
the sides. What must be its dimensions so that the cost of the can is least?
Let S be the closed parabolic bowl consisting of two pieces: S1: z = x2 + y2, x2 + y2 ≤ 1; and S2: x = rCos(ɸ), y = rSin(ɸ), z = 1 for 0≤ɸ≤2π, and 0≤r≤1. Let (the vector) F = (x-y+z)î + 2xĵ + k̂. Compute both sides of Gauss’s Divergence Formula (as given in the class) and show that they are equal.
Find the extreme values of z
on the surface 2x
2
+3y
2
+z
2
−12xy+4xz=35
A manufacturing process costs RM 6500 to set up for one year’s use. If items cost RM 85 each to produce and other costs amount to 3.5 x2, where x is the production in hundreds, find the level of production that will minimize the cost per item over the year. What will the total cost amount to at this level of production?
Apply separation of variable to solve
x2uxy+9y2u=0
Solve the Cauchy Problem,
xux+(x+y)uy=u+1 with u(x,y)=x2 on y=0
