### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# SI Calculus I MATH 1210

Weber State University

GPA 3.53

### View Full Document

## 15

## 0

## Popular in Course

## Popular in Math

This 2 page Class Notes was uploaded by Rosa Farrell on Wednesday October 28, 2015. The Class Notes belongs to MATH 1210 at Weber State University taught by Staff in Fall. Since its upload, it has received 15 views. For similar materials see /class/230806/math-1210-weber-state-university in Math at Weber State University.

## Similar to MATH 1210 at Weber State University

## Popular in Math

## Reviews for SI Calculus I

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 10/28/15

ADDITIONAL NOTES AND EXERCISES FOR 63 Newton7s method does not always work The following result gives suf cient conditions for when it does Theorem 1 Newton Let f ab A R be continuous Suppose that 0 for some c in ab Suppose that f exists and is bounded on ab39 that is there exists M gt 0 such that fI S M for every x E a b Suppose that f is bounded away from zero that is there exists 6 gt 0 such that f 2 e for every x 6 ab Then there is a closed interval I I d e C ab containing c such that the sequence given recursively by f1n71 In 7 Inil f 1n71 converges to c Moreover xn is in I for each n For this to make sense it helps if we have a notion of convergence of sequences We will do this in second semester calculus For now we will just use the intuitive statement as n gets large xn gets arbitrarily close to c77 and write xn c Let us now analyze the various conditions in the statement Bounding f away from zero should seem reasonable from the de nition of xn but it is not necessary The following exercise show that Newton7s method may work even if f is not bounded away from zero Exercise 2 Let x2 Adopt the notation of Newton7s theorem Show that if xn1 0 then xn 2 1 Suppose that x0 1 What is x1 How about x2 How about xn Argue that x7 converges to zero as n goes to 00 when x0 l In the above example any x0 except zero will do The next exercise illustrates what can go wrong if we do not bound f away from zero Exercise 3 Let x474x711 Then lt 0 lt so by the intermediate value theorem there exists a root between x 0 and x 3 What happens if we apply Newton7s method when we start at x0 1 Sketch the graph of f on the interval 0 3 We also require a bound on the second derivative The following exercise shows what can go wrong Exercise 4 Let xi Observe that x 0 is a root of Compute f x and explain why f is unbounded near x 0 Attempt to use Newtonls method with x0 1 What happens Illustrate your conclusion with a diagram 1 2 ADDITIONAL NOTES AND EXERCISES FOR 63 Newton7s method when it works is extremely fast The number of decimal places of accuracy approximately doubles with each successive iterationi The statement of Newton7s theorem does not tell us how to how to nd the closed interval 1 The proof gives some indication but is beyond the scope of the course For our purposes we can use a graphing calculator to give us an idea of where to look for the roots of a given function and then apply Newton7s method to get a good decimal approximation Exercise 5 Use Newton7s method to nd the coordinates of the in ection point 3 of y 772 sinz correct to six decimal places Exercise 6 Let a be a nonzero numberi Suppose we want to compute a decimal expansion of This could be dif cult if a is big or has a large number of decimal places Newton7s method gives us a way of computing a without divisioni et 1 7 7 a Notice that f has a root at z 7 Using the notation of Newton7s theorem show that 2 1 In 21ml 7 amnili

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "Selling my MCAT study guides and notes has been a great source of side revenue while I'm in school. Some months I'm making over $500! Plus, it makes me happy knowing that I'm helping future med students with their MCAT."

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.