Purchase Solution

Sets and absolute minimum

Not what you're looking for?

Ask Custom Question

Let S = {(x,y,z):2x-y+3z=6},p=(1,0,-1) belonging to R3, and let f:S->R be defined by f(q)=d(q,p),

ie, f(x,y,z)=sqrt((x-1)^2+y^2+(z+1)^2)

Question: Is S compact? Please verify if q belongs to S and q does NOT belong to [-5,5]^3, then f(q) >= 4.

ALSO prove that f attains its absolute minimum value at some point q0 belonging to S, and that q0 must be inside [-5,5]^3. (for this question I know you can use f(0,0,2) = sqrt(10) < 4)

Purchase this Solution

Solution Summary

This shows how to identify if S is compact, if a given term belongs to S, and also proves that a function attains absolute minimum value at a point in set S

Purchase this Solution

Free BrainMass Quizzes
Probability Quiz

Some questions on probability

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.