Recent content by KF33

Homework Statement: The homework problem is included below, but I am looking at the derivatives of vectors. Homework Equations: I have the properties of derivatives below, but not sure they help me here...

Homework Statement I am stuck on number 11 on my homework. Homework Equations Not Sure The Attempt at a Solution I know this has to have something to do with Riemann's Sum, but I am lost on where to start. I started by putting numbers in for p, but I think that is wrong.

Homework Statement Homework EquationsThe Attempt at a Solution I know I would have to do something with my calculator and I tried to solve like solving an equation for C, but not sure. I put all the matrices in my calculator. I then subtracted the first matrix to the other side then...

Homework Statement I have been working on the problem below and I am stuck. I am stuck primarily because of the part where is says x=0. If x-0, it should cancel everything out. The derivative of 0 is 0 so will cancel everything out I think, so I am not sure if that is the reasoning and the...

Is it enough to say an interval could be [-10,0]. Then I select x1 to be -9 and x2 to be -1. f(x1)=-.412 and f(x2)=-.841. I look and select k to be between those and find a c value which f(c)=k.

Homework Statement I need to show the attached function satisfies the Intermediate Value Property. Homework EquationsThe Attempt at a Solution I looked at the property definition, but I am really unsure what is being stated. I think if I knew what the property was stating, I could do the problem.

If there is at least one number c in [a,b] such that f(c)=k, then f is continuous on the closed interval [a,b] and k is any number between f(a) and f(b). I got the answer though I think.

Homework Statement I was given the problem of determining if the Converse of the Intermediate Value Theorem in my book was true. Below is my theorem from the book. Homework EquationsThe Attempt at a Solution I had looked at the converse and tried to draw some examples, and I am thinking it...

They are asking me to show f(x) is nowhere continuous. Well it is nowhere continuous because it is not continuous at each point in the interval. I think I got a now. would this work? Is this an idea of what you are getting at. ##\epsilon## = 1/2 ##\delta > 0## = 1/4 ##| |f(1/8)| - 0| <...

For "b" I was thinking 0, because when you look at the limit you see the following. $$\lim_{x \to 0} f(x) = 0$$ So the function would be defined at that point. For "a" I was thinking the absolute value function would be continuous, because I am thinking the -1 will change to positive 1.

Attached is the definition about limits. I think "a" is not continuous because the graph will be alternating between 1 and -1 and not stay at a straight line. I would have to pick up my pencil to draw the graph. For "b" I was thinking 0, because the limit as s approaches 0, the graph...

For "a" I was thinking it can't be continuous because the graph would be broken up and you technically could not draw the graph without picking up your pencil. For "b" I was thinking 0, but I think it is wrong.

Continuity at a point: A function f is continuous at c if the following three conditions are met. f(C) is defined lim as x approaches c exists. lim as x approaches c of f(x) = f(c)

Homework Statement The problem is posted below in the picture. I looked at c and d and can do those. I am unsure about a and b. Homework EquationsThe Attempt at a Solution I looked at graphing the problems, but I think it is a wrong approach.