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Algebra

Uniform Convergence of a Sequence

Let (f_n) be a sequence of continuous functions on R--->R^q which converges at each point of the set Q of rational numbers. If the set {f_n} is uniformly equicontinuous on R, show that the sequence converges at every point of R and that the convergence is uniform on every compact set of R. keywords: equi-continuous

Solve: The Slope of a Perpendicular Line

Consider the line x+5y = 5. Please address the following questions: What is the slope of a line perpendicular to this line? What is the slope of a line parallel to this line?

Solve the recurrence

Solve the recurrence T(n) = 2T(sqrt(n)) + 1 by making change of variables. The solution should be asymptotically tight. 2. Use a recursive tree to give an asymptotically tight solution to the recurrence T(n) = T(n-a) + T(a) + cn, where n > = 1 and c > 0 are constants.

Recursive Definitions

I want to get a better understanding of how these problems are done. For Exercises #1-3, decide whether the sequences described are subsequences of the Fibonacci sequence, that is, their members are some or all of the members, in the right order, of the Fibonacci sequence. 1. The sequence A(n), where A(n) = (n-1)2^n-2 +

Power Series

Expand (1-z)^-m in powers of z for m in N. Let (1-z)^-m=sum from n=0 to infinity of (a_nz^n) then a_n ~n^m-1/(m-1)! as n-> oo where ~ means that the quotient of the expressions to the left and the right of it tends to 1.

Solving Inequalities

Solve the inequality for W. Simplify your answer as much as possible. -(2/7)w + 9 ≥ 4w + 4

Algebra Questions

For 3y - 5x > 15 a) Find its slope. b) Find its y-intercept c) Is the line dashed or solid? d) Is the shaded area above or below the line? e) Write in slope-intercept form and standard form. (using only integers for standard forms). f) Does the point (1, -3) satisfy the inequality?

Finding the Equation of a Line

Find the equation of each line in the form y = mx + b if possible. The line through the origin that is perpendicular to the line through (-3, 0) and (0, -3)

How do you find the equation of a line?

Write an equation in slope-intercept form, if possible, for each line. 1. The line through (0, -2) that is parallel to the line y = -1/3x + 6. 2. The line through (0, 4) with slope -1/2.

Find the line through (-2,5) with slope -1.

Find the line through (-2,5) with slope -1. The solution of this problem which is given in the attached solution file gives a very clear and easy approach of solving this type of solutions and the students can use this solution as a model to solve other similar problems.

Solving Differential Equations

Please help solve this seperable equation and a possible suggestion on how to look for factors to multiply by in order to make it exact. (x+y)dx - xdy = 0

What is the hottest temperature reached?

The temperature inside a kiln used to bake clay pottery is given by T(x) = -0.4x^2 + 32x + 73 degrees F where x is the number of minutes the kiln is on and 0 <= x <=80. (see equation in attached file)