Find the Taylor polynomial {image} for the function f at the number a = 1. f(x) = ln(x)

Nov 20, 2014

40 likes | 139 Views

1. 2. 3. Find the Taylor polynomial {image} for the function f at the number a = 1. f(x) = ln(x). {image} {image} {image}. 1. 2. 3. Find the Taylor polynomial {image} for the function f(x) at the number a = 4. {image}. {image} {image} {image}.

Share Presentation

Embed Code

Link

image
image image
accuracy r2
accuracy r3
taylor polynomial image

dalton-beck

Download Presentation

Find the Taylor polynomial {image} for the function f at the number a = 1. f(x) = ln(x)

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

1. 2. 3. Find the Taylor polynomial {image} for the function f at the number a = 1. f(x) = ln(x) • {image} • {image} • {image}
1. 2. 3. Find the Taylor polynomial {image} for the function f(x) at the number a = 4. {image} • {image} • {image} • {image}
Use Taylor's Inequality to estimate the accuracy |R2| of the approximation f(x) at the number a = 1, when {image} {image} • 0.0068 • 1.0068 • 0.5068
Use Taylor's Inequality to estimate the accuracy |R3| of the approximation f(x) at the number a = 0, when {image} {image} • 1.0001 • 0.5001 • 0.0001

Zeros of Polynomial Functions

Zeros of Polynomial Functions. Objectives: Use the Fundamental Theorem of Algebra to determine the number of zeros of polynomial functions Find rational zeros of polynomial functions Find conjugate pairs of complex zeros Find zeros of polynomials by factoring

893 views • 30 slides

ُ The polynomial project

ُ The polynomial project. Task1: find the polynomial that gives the following value. P(X)=A+B(X-X 0 )+C(X-X 0 )(X-X 1 )+D(X-X 0 )(X-X 1 )(X-X 2 ). a. Write the system of equations in A,B,C, and D that you can use to find desired polynomial. 10 =A -6 =A+B(1+1) -17 =A+B(2+1)+C(2+1)(2-1)

316 views • 18 slides

Topic #6: Polynomial Equations

Topic #6: Polynomial Equations. Drill. Find the zeros of the following function (in factored form) Find a quadratic equation (in polynomial form) with zeros at -3, and 4. Factor the following polynomial equation, then identify the zeros:. Topic #6 Objectives.

445 views • 30 slides

Basics of a Polynomial

Basics of a Polynomial. Polynomial. An expression involving a sum of whole number powers multiplied by coefficients: a n x n + … + a 2 x 2 + a 1 x + a 0 Ex: What are examples of polynomials that we have used frequently?. Quadratics:. Linear:. Zero or Root of a Polynomial.

520 views • 21 slides

Zeros of Polynomial Functions

Zeros of Polynomial Functions. The Fundamental Theorem of Algebra The f(x) is a polynomial of degree n, where n > 0, then f has at least one zero in the complex number system. That is, in the complex number system, every nth-degree polynomial function has precisely n zeros.

284 views • 11 slides

Warm-Up: November 27, 2012

Warm-Up: November 27, 2012. Solve x 3 +2x 2 -2x-1=0. Homework Questions?. Zeros of Polynomial Functions. Section 7.5. Essential Question. How can we find every zero of a polynomial function?. Improved Guess and Check. There are a limited number of possible rational roots of a polynomial.

523 views • 31 slides

5.2 Evaluate and Graph Polynomial Functions

5.2 Evaluate and Graph Polynomial Functions. Common Polynomial Functions. Identify Polynomial Functions. Determine whether the function is a polynomial function. If so, state if it’s in standard form, it’s degree, type, and leading coefficient.

363 views • 9 slides

6.2 Evaluating and Graphing Polynomial Functions Turn to page 329 Goal 1:

6.2 Evaluating and Graphing Polynomial Functions Turn to page 329 Goal 1: Evaluate a Polynomial Function. Goal 2:Pg. 329 Graph a polynomial function by hand. E VALUATING P OLYNOMIAL F UNCTIONS. a n. n. n. n – 1. a 0. a n  0. leading coefficient. a n. constant term. degree.

317 views • 17 slides

Hellman’s Algorithm

Hellman’s Algorithm. Time / Memory tradeoff for finding a pre-image of a random function June 2011 Weizmann Institute of Science. Problem definition. For any function f: {0,…,N-1}:{0,…,N-1} , given a value y from the image , find a pre-image x such that f(x)=y .

188 views • 9 slides

Find the average value of the function {image} on the interval [1, 4].

1. 2. 3. 4. Find the average value of the function {image} on the interval [1, 4]. {image} {image} {image} {image}. True or False: If u(v) is continuous and {image} , then u(v) takes on the value -7 at least once on the interval [2, 10]. True False. 1. 2. 3. 4.

114 views • 4 slides

Accuracy in Series

Accuracy in Series. Lesson 9.7B. Remainder of a Taylor Polynomial. We need a sense of how accurate our approximation is Actual Approximate Remainder Function Value. Remainder of a Taylor Polynomial. Error associated with the approximation

196 views • 10 slides

Polynomial Functions

Polynomial Functions. A polynomial function is a function of the form f(x)= a n x n +a n-1 x n-1 +…a 1 x 1 +a 0. A power function. A power function of degree n is a function in the form f(x) = ax n where a is a real number, a ≠ 0 and n > 0 is an integer.

1.48k views • 10 slides

AP Calculus BC – Chapter 9 - Infinite Series 9.3: Taylor’s Theorem

AP Calculus BC – Chapter 9 - Infinite Series 9.3: Taylor’s Theorem. Goals : Approximate a function with a Taylor polynomial. Analyze the truncation error of a series using graphical methods or the Remainder Estimation Theorem. Use Euler’s formula to relate the functions sinx, cosx, and e x.

448 views • 7 slides

Lecture 5I Function Approximation

Lecture 5I Function Approximation. Data driven function approximation Projective hyper-tangent function. Interpolation vs approximation. Polynomial interpolation Constraints: f(x i )=y i for all I Polynomial approximation Minimization of mean square error Non-polynomial approximation

462 views • 21 slides

1. Polynomial Functions

1. Polynomial Functions. Polynomial functions have multiple terms with bases raised to different powers The degree of the polynomial function is the highest exponent in the equation 2 nd degree and higher polynomials are non-linear functions

436 views • 13 slides

Polynomial Functions Zeros and Graphing

Section 2-2. Polynomial Functions Zeros and Graphing. Objectives. I can find real zeros and use them for graphing I can determine the multiplicity of a zero and use it to help graph a polynomial I can determine the maximum number of turning points to help graph a polynomial function.

453 views • 13 slides

Polynomial Functions

Polynomial Functions. E VALUATING P OLYNOMIAL F UNCTIONS. a n. n. n. n – 1. a 0. a n  0. leading coefficient. a n. constant term. degree. a 0. n. descending order of exponents from left to right. A polynomial function is a function of the form.

507 views • 36 slides

Chapter 2 Polynomial, Power, and Rational Functions

Chapter 2 Polynomial, Power, and Rational Functions. Group Practice. Polynomial Function. Note:. Remember Polynomial Poly = many Nomial = terms So it literally means “many terms”. Name Form Degree Zero Function f(x)=0 Undefined Constant Function f(x)=a ( a ≠0) 0

1.87k views • 164 slides

The Polynomial Project

The Polynomial Project. Math Project. Task 1. Find the polynomial that gives the following values ➪. p(x)= A+b (x-x 0 )+C(x-x 0 )(x-x 1 )+D(x-x 0 )(x-x 1 )(x-x 2 ). a . Write the system of equations in A,B,C, and D that you can use to find the desired polynomial.

514 views • 17 slides

Objectives: 1. Be able to graph a polynomial function using calculus.

Objectives: 1. Be able to graph a polynomial function using calculus. Critical Vocabulary: Polynomial Function, End Behavior, Intercepts, Multiplicity, Critical Numbers, Extrema, Inflection Points, Concavity, Domain, Range. Example 1. Graph f(x) = x 4 - 12x 3 + 48x 2 – 64x.

308 views • 13 slides

Warm up 1

Find the product of the following ( x + 4)(x + 7 ) 2 . 3. Identify the following from the expression Number of terms Type of Polynomial ( monomial, binomial, trinomial, polynomial) Leading Coefficient. Warm up 1. What do all of these have in common?. They are FISH!.

200 views • 11 slides

More Related