My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
January 4th, 2015, 09:59 PM   #1
Senior Member
 
Joined: Sep 2013
From: Earth

Posts: 827
Thanks: 36

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?

Last edited by greg1313; January 4th, 2015 at 11:02 PM.
jiasyuen is offline  
 
January 4th, 2015, 10:58 PM   #2
Global Moderator
 
greg1313's Avatar
 
Joined: Oct 2008
From: London, Ontario, Canada - The Forest City

Posts: 7,641
Thanks: 959

Math Focus: Elementary mathematics and beyond
It's intermediate value theorem, not "Immediate Value Theorem".

Since one can find values where tan(x) - 2x is negative and where tan(x) - 2x is positive in the
given interval, at some point in the given interval tan(x) - 2x = 0 (by the intermediate value theorem).

I don't know how much detail is required to provide an acceptable answer your question.
greg1313 is offline  
January 4th, 2015, 11:16 PM   #3
Newbie
 
Joined: Jul 2012
From: Houston, Texas

Posts: 18
Thanks: 2

Math Focus: Geometry , Modern Algebra
I will give a try.
Take the function $f(x) = \tan(x) - 2$
We know that $f(x)$ is continuous on the interval $(0,1.4)$
Because this is an open interval, we can't choose 0 and 1.4. Pick two value x= $0.1$ and $x =1.39$ to test the sign of $f(x)$.
At $x = 0.1, f(0.1) < 0$
At $x = 1.39, f(1.39) > 0$
The Intermediate Value Theorem states that if $f(a).f(b) <0$ then there exist an $x$ between$ (a,b)$ such that $f(x) = 0.$
The problem can also be solve by using Intermediate Value Theorem for Derivative.

Last edited by skipjack; January 5th, 2015 at 07:10 AM.
buiduchuy is offline  
January 5th, 2015, 06:11 AM   #4
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,031
Thanks: 2342

Math Focus: Mainly analysis and algebra
Strictly speaking, this is Bolzano's theorem which is a special case of the intermediate value theorem.
v8archie is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
intermediate, theorem



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Remainder Theorem + Factor Theorem righen Algebra 3 January 23rd, 2014 09:19 AM
Mean Value Theorem Ozgur Applied Math 1 January 5th, 2012 01:26 PM
Mean Value Theorem Ozgur Calculus 4 December 29th, 2011 06:04 AM
Mean Value Theorem Ozgur Abstract Algebra 3 December 28th, 2011 03:07 PM
proof by using greens theorem or stokes theorem george gill Calculus 5 May 14th, 2011 03:13 PM





Copyright © 2017 My Math Forum. All rights reserved.