# intermediate

1. ### Intermediate Value Theorem

question: Is there a number that is exactly 5 more than its cube? What I tried : x=number x+5=x^3 if we rearrange: x^3-x-5 after here I think I need to plug in two consequent numbers?(how do I pick that two numbers?) to see x^3-x-5<0 and x^3-x-5>0 and?
2. ### Intermediate Value Theorem

The question attached below. I tried to solve it with piecewise linear function but I still can't. Can someone help me?
3. ### Intermediate Value Theorem Problem

I know this problem is to do with the IVT but I'm not sure where to start- could somebody please give me a hint- thanks Suppose that F: R---> R is continuous at every point. Prove that the equation F(x) = c cannot have exactly two solutions for every value of c.
4. ### Intermediate Value Theorem

Use the Immediate Value Theorem to show that there is a root of the given equation in the specified interval. tan(x)=2x (0,1.4) How to solve this question?
5. ### Question related to the Intermediate value theorem

Suppose that f:[0,1] \times [0,1] \rightarrow \mathbb{R}. I know that f is C^{1,1} and also that for each given y \in [0,1] there exists x_{y} \in [0,1] such that f(x_{y},y)=0. By the Intermediate value theorem it follows that there exists open set U containing x_{y} and open set V containing...
6. ### Intermediate value theorem

A manatee leaves his home at 7a.m. and swims along a well travelled path until he reaches a friend's home 10 hours later (where an all night manatee party ensues). The next day the manatee leaves his friend's house at 7a.m. and returns home in the same amount of time taking the same path. If...
7. ### Intermediate Value Theorem

Hi all :) Strange question here involving the intermediate value theorem. Consider the equation x^3 + x +e^x = 0 Use the intermediate value theorem to show there is a solution on the interval (-1,0) and show that there is exactly one real solution of the equation. I've been trying at this...
8. ### intermediate value theorem

For the following proof of the intermediate value theorem ,which i found in wikipedia: Proof: Let S be the set of all x in [a, b] such that f(x) ? u. Then S is non-empty since a is an element of S, and S is bounded above by b. Hence, by completeness, the supremum c = sup S exists. That is, c is...
9. ### Fin. gen field extension -> intermediate field f.g. also?

If k\subseteq E\subseteq K if an extension of fields, with K finitely generated over k, how can I go about showing that E must also be finitely generated over k? I've tried just some basic degree stuff and looked at examples, but I'm not getting anywhere on this one.. perhaps induct on the...
10. ### Intermediate Algebra

Hello, I have a test day after tomorrow. I have been sick for the past two weeks so I wasn't able to go to classes. Our professor gave us a test with the same problems that are gonna be on the test and we can have notes. The thing is that this doesn't help me since I don't know how to solve...
11. ### continuous and intermediate value theorem

assume f:R->R has this property A at c when, for each ?>0 there exists a ??0, s.t. |x-c|?? implies |f(x)-f(c)|??. Show that every function has this property at every c, c is real number (i know when ?=0 ,then x=c we have f(x)-f(c)=0<?, but how about f(x)-f(c)=? i don't know how to start it )
12. ### continuous and intermediate value theorem

use the intermediate value theorem to prove that if f,g are continuous functions on [o,1]wih f(1)=g(0) and f(0)=g(1),then there exists x belongs[0,1] with f(x)=g(x)
13. ### Intermediate Values

Suppose that f is continuous on [0,1], and maps [0,1] into [0,1] Take any point c in [0,1] and define a sequence {Xn} inductively by X1= c, Xn+1=f(Xn). Suppose that {Xn} converges to the point p. Prove that p is a fixed point of f(x) I have no idea how this works.. smart people please HELP!
14. ### intermediate value theorem function

Let f be a continuous function on A={x \in \mathbb{R}^2: ||x||=1} \cup {x \in \mathbb{R}^2: ||x-(2,0)||_1 \leq 1. f(-1,0)=-1 and f(3,0)=17. Prove that exists a \in A that f(a)=0. Are there any funcitions like above but there is only one such point a? The first part of problem is quite...
15. ### Intermediate value theorem to show tanh bijection property

How would we use the Intermediate Value Theorem to prove that tanh: R\rightarrow (-1,1) is a bijection
16. ### limit of an intermediate form

I want to find cos^2 x/2^x as x approaches infinity My first instinct is to use L'Hospitals rule and differentiate unfortunately this leads to -2 sin x cos x/(ln 2 2^x) Which is utterly unhelpful I'm really stuck on this one. If anybody has any insight I would really appreciate BTW from a...
17. ### Help with the Intermediate Value Theorem

"Use the Intermediate Value Theorem to show that there is a solution to the equation in the specified domain: tan(x) = 4x-1 on (0, pi/4)
18. ### Intermediate values theorem

Here's a spectacular, though very easy, application of the intermediate values theorem: prove that there exist two diametrically opposed points of the earth with equal temperature (assuming the temperature is continuously distributed, and assimilating the earth to a perfect 3 dimensional ball).