MYTUTOR SUBJECT ANSWERS

311 views

Use the Intermidiate Value Theorem to prove that there is a positive number c such that c^2 = 2.

This exercise is asking to prove the existance of the square root of 2. So let's consider the function f(x) = x^2. Since f(x) is a polynomial, then it is continuous on the interval (- infinity, + infinity). Using the Intermidiate Value Theorem, it would be enough to show that at some point a f(x) is less than 2 and at some point b f(x) is greater than 2. For example, let a = 0 and b = 3. Therefore, 

f(0) = 0, which is less than 2, and f(3) = 9, which is greater than 2. Applying IVT to f(x) = x^2 on the interval [0,3] and taking N=2, we can therefore guarantee the existance of a number c such that 0

Dilyana K. GCSE Maths tutor, GCSE Physics tutor

11 months ago

Answered by Dilyana, a GCSE Maths tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

330 SUBJECT SPECIALISTS

£18 /hr

Jack G.

Degree: Politics, Philosophy, and Economics (Bachelors) - Warwick University

Subjects offered: Maths, Religious Studies+ 2 more

Maths
Religious Studies
Economics
.TSA. Oxford.

“Hello, I'm Jack and am studying politics, philosophy, and economics at Warwick.  Having recently been through the subjects I'm looking to tutor I feel like I know first hand what difficulties you'll be facing. I always found I wanted ...”

MyTutor guarantee

£18 /hr

Kilda C.

Degree: Medicine (Bachelors) - Oxford, New College University

Subjects offered: Maths, Physics+ 2 more

Maths
Physics
Chemistry
Biology

“Hello! I'm Kilda, I come from Belgium and I'm about to start my third year readingMedicine at the University of Oxford. I have been tutoring Science, Maths, Piano and Music Theory since 2011. When I am tutoring, or trying to learn som...”

£18 /hr

Victoria E.

Degree: Economics (Bachelors) - Bristol University

Subjects offered: Maths, Science+ 4 more

Maths
Science
Human Biology
Chemistry
-Personal Statements-

“Hi,I'm an enthusiastic student studing Economics at the University of Bristol. For my A Levels I studied Maths, Biology and Chemistry and would love to help younger students at GCSE level in these subjects.During sixth form I tutor...”

About the author

Dilyana K.

Currently unavailable: for regular students

Degree: Computer Science (Bachelors) - Edinburgh University

Subjects offered: Maths, Physics

Maths
Physics

“Why choose me for your personal guide into the science? Well, I have been studying math and physics very intensively in high school and I was prepared by the best teachers in my country. Competitions have become an integral part of my...”

You may also like...

Posts by Dilyana

Two identical objects have a charge of magnitude q. If r is the distance bethween them, what should their mass be so that the objects are balanced.

Use the Intermidiate Value Theorem to prove that there is a positive number c such that c^2 = 2.

Other GCSE Maths questions

What is the mean of the numbers: 1, 7, 25, 9 and 34?

You are given a square which you are told has a total area of 100 squared centimetres. You are also told that one side of the square has dimension 4(3x + 2), and the other has dimension 8x - y. What are the values of x and y?

Solve the two simultaneous equations: 2y + x = 8 [A] and 1 + y = 2x [B]

Solve the inequality 5x+3<3x-6

View GCSE Maths tutors

Cookies:

We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok