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let F = (x^2+y^2+z^2)^n * (xi+yj+zk) for F, i, j, k vectorsand let Omega be the sphere of radius b centered on the origin
i) calculate the outward flux of F across the boundary dOmegaii) calculate the divergence of Fiii) referring to (i) and (ii), what is special about the value n = -3/2?
Who gets to the door first? How many turns does it take each student to reach the door.
Describe the kernel of the linear transformation T:P1to r defined by T(p)= definite integral from 0 to 1 p(x)dx where P1 is the set of continuous linear function on [0,1], and R is the set of real numbers.
If Tom Bombadil's house is 15 miles east of Hobbiton and 8 miles south, what is the straight line distance (omit units)?
What are the different forms of linear equations in two variables? Show an example of each form. How does the sign or value of the slope determine its type (i.e. whether it is +ve, -ve, undefined, or zero)?
Suppose the velocity v (in m/s) of a some moving object can be computed by the formula v=10t+4, where t (in s) is the time elapsed. What is the biggest possible error (worst case) of v if the error in the measurement of t is known to be less than 0..
Angie's puppy weighed 3kg when she first got it. Two years later it weighed 9kg. How many grams of weight did the puppy gain.
Probabilities of Selecting Multiples of Fixed Numbers. Let N = 1000 and let S = {1, 2, ... , N}. Let D_i = {m belongs to S: i|m} for integers i between 1 and N.
The peremiter of a cross section of a piece of lumber is 34 1/2 in. The length is twice the width. Find the actual dimension of the cross section of this piece of lumber.
Let f (x) = |x| for x greater or equal to -1, less than or equal to +1. Write the Fourier series for f (x) on [-1,1]. Show that this series can be differentiated term by term to yield the Fourier expansion of f'(x) on [-1,1]
Label the Vertex and the Axis of symmetry
Which pair has equally likely outcomes? List the letters of the two choices below which have equal probabilities of success, separated by a comma.
Combine from JPE, Fall 90 and Spring 97) Let A ∈ C^(n X n) be a normal matrix. Prove that A - M is normal for any λ ∈ C. Prove that ||Ax||2 - ||∧*x||2 for all x ∈ C^n
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