Clicker Question 1 What is the degree 2 (i.e., quadratic) Taylor polynomial for f (x) = 1 / (x + 1) centered at 0? – A. 1 + x – x 2 / 2 – B. 1  x – C.

Slides:

Advertisements

Similar presentations

Make sure you know the day and time of the final exam for this section of Math 110: Day: ______ Date:______ Time: ______ to _______ All Math 110.

Advertisements

Please CLOSE YOUR LAPTOPS, and turn off and put away your cell phones, and get out your note-taking materials. Today’s daily quiz will be given at the.

Any questions on the Section 5.2 homework?. Please CLOSE YOUR LAPTOPS, and turn off and put away your cell phones, and get out your note- taking materials.

Clicker Question 1 The function f (x ) is graphed on the board. If the derivative function f '(x ) were graphed, where would it intersect the x – axis?

Taylor Series (11/12/08) Given a nice smooth function f (x): What is the best constant function to approximate it near 0? Best linear function to approximate.

Announcements DS-533 Fall Week 1: August 25 Read: –Business Forecasting Chapter 2 Do problems: –3, 5, 7, 9, 12, Hand-in assignments –4, 8, 14.

Integration – Adding Up the Values of a Function (4/15/09) Whereas the derivative deals with instantaneous rate of change of a function, the (definite)

Integrals and the Fundamental Theorem (1/25/06) Today we review the concepts of definite integral, antiderivative, and the Fundamental Theorem of Calculus.

Clicker Question 1 What is the unique antiderivative of f (x ) = 1 / x 2 whose value is 4 when x = 1 ? A. -1 /x + 5 B. -1 /x + 4 C. -1 /x + 3 D.

Look Ahead Today – HW#4 out Monday – Regular class (not lab) Tuesday – HW#4 due at 4:45 Wednesday – Last class - return clickers Thursday – Regular office.

Look Ahead (4/27/08) Tuesday – HW#4 due at 4:45 Wednesday – Last class – return clickers, review and overview, and do evaluations. Thursday – Regular office.

Taylor Series (4/7/06) We have seen that if f(x) is a function for which we can compute all of its derivatives (i.e., first derivative f '(x), second derivative.

Please close your laptops and turn off and put away your cell phones, and get out your note-taking materials. Today’s daily homework quiz will be given.

Please open your laptops, log in to the MyMathLab course web site, and open Quiz 5.5A. You may use the formula sheet on this quiz – please don’t write.

Please open your laptops and pull up Quiz Only the provided online calculator may be used on this quiz. You may use your yellow formula sheet for.

Make sure you know the day and time of the final exam for this section of Math 110: Day: ______ Date:______ Time: ______ to _______ All Math 110 finals.

Please open your laptops, log in to the MyMathLab course web site, and open Quiz 5.1. You may use the pink formula sheet on this quiz – please don’t write.

Please CLOSE YOUR LAPTOPS, and turn off and put away your cell phones, and get out your note-taking materials. Today’s daily quiz will be given at the.

 To add numbers in scientific notation: 1) Add the constants 2) Keep the exponent the same  Example: (2.1 x 10 5 ) + (3.2 x 10 5 ) = ( ) x 10.

Please open Daily Quiz 34. A scientific calculator may be used on this quiz. You can keep your yellow formula sheets out when you take the quiz. Remember.

4/29 Finish grade FRQ’s and go over test I check review manual practice exam – need %’s both sections Homework – Concentrate on your STAR tests – look.

SWBAT… compute problems involving zero & negative exponents Mon, 4/4 Agenda 1. WU (5 min) 2. Midterms Results/ Calendar / Reminders / Expectations (10.

Taylor’s Polynomials & LaGrange Error Review

Find the local linear approximation of f(x) = e x at x = 0. Find the local quadratic approximation of f(x) = e x at x = 0.

Polynomial Approximations BC Calculus. Intro: REM: Logarithms were useful because highly involved problems like Could be worked using only add, subtract,

Consider the following: Now, use the reciprocal function and tangent line to get an approximation. Lecture 31 – Approximating Functions

Clicker Question 1 – A. converges to 1 – B. converges to 1/5 – C. converges to -1/5 – D. converges to 5 – E. diverges.

Do Now: Find both the local linear and the local quadratic approximations of f(x) = e x at x = 0 Aim: How do we make polynomial approximations for a given.

Lecture 11.   Modular arithmetic is arithmetic in which numbers do not continue forever.  Modulo 7 has numbers 0, 1, 2, 3, 4, 5, and 6.  Modulo 5.

Clicker Question 1 What is the instantaneous rate of change of f (x ) = ln(x ) at the point x = 1/10? A. 1/10 B. 10 C. 0 D. ln(1/10) E. undefined.

Time-Series Forecasting Overview Moving Averages Exponential Smoothing Seasonality.

Calculus I – Course Syllabus Class Periods: 1:00pm-1:50am MTWF Classroom: Thompson Hall 315 Instructor: Mei Q. Chen, Thompson Hall 230

Test Corrections You may correct your test. You will get back 1/3 of the points you lost if you submit correct answers. This work is to be done on your.

Please CLOSE YOUR LAPTOPS, and turn off and put away your cell phones, and get out your note- taking materials.

PROPERTIES OF EXPONENTS

Retakes: -Turn in quiz corrections -Retakes Thursday and Friday at lunch, or as arranged before the end of next week. Today’s Plan -Correct -Combining.

MARCH 19, 2012 AP CALCULUS. STUDY DAVIESS CO. I have the following going on Saturday: Rachel Tanner Haley Ross Anyone else? Meet in teacher’s.

Clicker Question 1 What is the exact average value of f(x) = 1/x 2 between x = 1 and x = 3? – A. 1/3 – B. 2/3 – C. 2/9 – D. ln(3) – E. ln(3)/2.

Please CLOSE YOUR LAPTOPS, and turn off and put away your cell phones, and get out your note- taking materials.

Monday Schedule Monday: Rational Equations Tuesday: Rational Equations Wednesday: In class Activity, Factoring Quiz Thursday: Quiz Friday:

DO NOW – WALL COVERING WEDNESDAY. OPERATIONS WITH POLYNOMIALS 12/9/2015.

Clicker Question 1 – A. converges to 3/4 – B. converges to 1/4 – C. converges to 1/12 – D. converges to 1 – E. diverges.

REMINDER: If you haven’t yet passed the Gateway Quiz, make sure you take it this week! (You can find more practice quizzes online in the Gateway Info menu.

Clicker Question 1 What is the derivative of f (x ) = 2x sin(x ) ?

Derivative Facts (1/23/12) d/dx (x r ) = ( provided r is what?) d/dx (a x ) = d/dx ( sin(x )) = d/dx (cos(x )) = d/dx (tan(x )) = d/dx (sec(x )) = d/dx.

Announcements DS-203 Spring Week 1: January 18, 2009 Read: –The practice of Business Statistics: Using Data for Decisions Chapter 1, sections 1.

9.1 B Power Series. This series would converge of course provided that … Write f (x) as a series: This looks like the sum of… A Geometric Series: in which.

Please CLOSE YOUR LAPTOPS, and turn off and put away your cell phones, and get out your note-taking materials.

1 College Algebra K/DC Friday, 08 April 2016 OBJECTIVE TSW solve exponential equations. Put assignment in wire basket, please ! QUIZ: Sec. 4.4 will be.

REMINDER: If you haven’t yet passed the Gateway Quiz, make sure you take it this week! (You can find more practice quizzes online in the Gateway Info menu.

Any questions on the Section 5.4 homework?. Please CLOSE YOUR LAPTOPS, and turn off and put away your cell phones, and get out your note- taking materials.

Please CLOSE YOUR LAPTOPS, and turn off and put away your cell phones, and get out your note- taking materials.

Grade Scale Quiz 3 Results: Average class score after partial credit: XX.X% Commonly missed questions: # ____________________ We will be going over some.

Chapter 3 Lect 6 Forecasting. Seasonality – Repetition at Fixed Intervals Seasonal variations –Regularly repeating movements in series values that can.

Clicker Question 1 What is ? (Hint: u-sub) – A. ln(x – 2) + C – B. x – x 2 + C – C. x + ln(x – 2) + C – D. x + 2 ln(x – 2) + C – E. 1 / (x – 2) 2 + C.

MTH 253 Calculus (Other Topics) Chapter 11 – Infinite Sequences and Series Section 11.8 –Taylor and Maclaurin Series Copyright © 2009 by Ron Wallace, all.

Please CLOSE YOUR LAPTOPS, and turn off and put away your cell phones, and get out your note- taking materials.

Warm Up Determine the interval of convergence for the series:

Lecture 25 – Power Series Def: The power series centered at x = a:

Taylor series in numerical computations (review)

Multiplying Polynomials

Adding and Subtracting Polynomials (9.1)

Taylor and MacLaurin Series

Clicker Question 1 What is the interval of convergence of A. (-, )

Clicker Question 1 What is the degree 2 (i.e., quadratic) Taylor polynomial for f (x) = 1 / (x + 1) centered at 0? A. 1 + x – x 2 / 2 B. 1  x C. 1 

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

Clicker Question 1 What is the interval of convergence of A. (-, )

Clicker Question 1 Given: f(x) = 1 + x + x2/2 + x3/3! + x4/4!, g(x) = x - x3/3! + x5/5!, and h(x) = (x –1) – (x –1)2/2 + (x –1)3/3 – (x –1)4/4.

Taylor Series and Maclaurin Series

Section 11.6 – Taylor’s Formula with Remainder

Presentation transcript:

Clicker Question 1 What is the degree 2 (i.e., quadratic) Taylor polynomial for f (x) = 1 / (x + 1) centered at 0? – A. 1 + x – x 2 / 2 – B. 1  x – C. 1  x + x 2 – D. 1  x + 2x 2 – E. 1 – x + x 2 / 2

Clicker Question 2 What is the degree 2 (i.e., quadratic) Taylor polynomial for f (x) =  x centered at 1? – A. 1 + x / 2 – x 2 / 8 – B. 1 + (x – 1) / 2 – (x – 1) 2 / 4 – C. 1 + (x – 1) / 2 – (x – 1) 2 / 8 – D. 1 – (x – 1) / 2 + (x – 1) 2 / 8 – E. 1 + x / 2 – x 2 / 8

End of Semester Schedule Hand-in #5 will go out Friday, Apr 30 and be due at 4:45 pm on Tuesday, May 4. Corrected homework, clicker score, and average coming into the final exam will be available by 3:15 on Thursday, May 6. Regular office hours through next week (Tu & Th 3:15-4:45). Also Monday, May 10, 3:00-5:00. Optional review session 12:20-1:15 on Friday, May 7. Exam is Tuesday, May 11 from 9 to noon (here). You may bring TWO reference sheets.

How Calculators Work (4/28/10) Hand calculators can add, subtract, multiply, divide, and raise to whole powers easily. They can easily store constants like the values of e, , ln(10), and so on. In order to compute the values of power functions to non-whole exponents and to compute any of the transcendental functions, calculators useTaylor Series! (Actually, Taylor polynomials.)

Working Near the Center Taylor series are exact, but Taylor polynomials are approximations, and they are most accurate near the center of the interval of convergence. Hence calculators do what they can be applying the Taylor polynomial to an argument as close to the center as possible. How? It depends on the function.

An Example: The Sin Function Sin is periodic, with period 2 , and calculators know that. The standard Taylor series for the sin is centered at 0, so we alter the argument to be as near 0 as possible. What can a calculator do to get the best estimate of sin(34)?

Another Example: ln(x) The standard Taylor series for ln(x) is centered at 1 and only converges on (0, 2), so to apply this technique the argument must be within that interval. What can a calculator do to get the best estimate of ln(834)? (Calculators can be taught the rules of logs, of course.)

Assignment for Friday Assignment (not hand-in) is handed out.