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Section 11.4 – Representing Functions with Power Series
4.Find the power series representation for centered about x = 0 and specify its radius of convergence. Infinite geometric with first term 1/3 and r = -2x/3 Converges when |r| < 1
8. Find the power series representation for centered about x = 0 and specify its radius of convergence. Radius of Convergence is 1
12. Use the power series representation of power series representation of the function to produce a
18.Find a power series representation of f(x) = ln x centered at x = 1. Specify the radius of convergence of the power series. Radius of convergence is 1
26.Use an appropriate identity to find the Maclaurin series for f(x) = sin x cos x
30. Given the function f defined by a.Find the first three nonzero terms in the Maclaurin series for the function f.
30. Given the function f defined by b. Find the first three terms in the Maclaurin series for the function g defined by
30. Given the function f defined by b. Find the first four terms in the Maclaurin series for the function h defined by
Section 11.6 – Taylor’s Formula with Remainder. The Lagrange Remainder of a Taylor Polynomial where z is some number between x and c The Error of a Taylor.
Arithmetic and Geometric Means OBJ: Find arithmetic and geometric means.
DO NOW: Find the volume of the solid generated when the region in the first quadrant bounded by the given curve and line is revolved about the x-axis.
L’Hopital’s Rule (62) Note that the quotient is still indeterminate at x = π/2. We removed this indeterminacy by cancelling the factor − cos x.
THEOREM 2 Sum of a Geometric Series Let c 0. If |r| < 1, then If |r| ≥ 1, then the geometric series diverges. Sum of an Infinite Geometric Series (80)
Differentiation Department of Mathematics University of Leicester.
Section 11.5 – Testing for Convergence at Endpoints.
Resultant of two forces Resultant of parallel forces Resultant of perpendicular forces Resultant two forces at any angle Learning objectives.
Geometric Series Starter. Write down the algebraic expression for a geometric series a + ar + ar 2 + ar 3 + … + ar n-1.
Maths C4 Binomial Theorem. Three quick questions from C2 Expand the following: 1) (1+x) 4 2) (1-2x) 3 3) (1+3x) 4 Here these expansions are finite (n+1)
1 To find the x-intercepts of y = f (x), set y = 0 and solve for x. INTERCEPTS AND ZEROS To find the y-intercepts of y = f (x), set x = 0; the y-intercept.
DCSP-11 Jianfeng Feng
12.3 Infinite Sequences and Series. Infinite sequence – a sequence that has infinitely many terms. Infinite sequence – a sequence that has infinitely.
Recursive & Explicit Formulas January 5 – 7, 2010.
Chapter 8 Vocabulary. Section 8.1 Vocabulary Sequences An infinite sequence is a function whose domain is the set of positive integers. The function.
Summary of Convergence Tests for Series and Solved Problems Integral Test Ratio Test Root Test Comparison Theorem for Series Alternating Series.
Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1 Section 5.1 Adding and Subtracting Polynomials Copyright © 2013, 2009, 2006 Pearson Education, Inc.
ALGEBRAIC EXPRESSIONS Step 1Write the problem. Step 2Substitute in the values for the unknown (variable). Step 3Use PEMDAS (remember to go left to right).
Power Series. So, start asking yourself this question: Can x be 0, 1 / 2, – 1 / 2, 3 / 4, – 3 / 4, 1, –1, 3 / 2, – 3 / 2, 2, –2, and so on? Power SeriesIntroduction.
13.3 T RIG FUNCTIONS OF GENERAL ANGLES Algebra II w/ trig.
12.7 (Chapter 9) Special Sequences & Series. Fibonacci Sequence: 1, 1, 3, 5, 8, 13, … Describes many patterns of numbers found in nature. a 1 = 1 and.
12.1 – Arithmetic Sequences and Series. An introduction………… Arithmetic Sequences ADD To get next term Geometric Sequences MULTIPLY To get next term Arithmetic.
Unit 6. For x 0 and 0 a 1, y = log a x if and only if x = a y. The function given by f (x) = log a x is called the logarithmic function with base.
11.1 Mathematical Patterns. Ex 1 Start with a square with sides 1 unit long. On the right side, add on a square of the same size. Continue adding one.
Sequences. Infinite Sequences Limits of Infinite Sequences Arithmetic and Geometric Sequences Sequences and Graphing Calculators … and why Infinite.
11.2 P ROPERTIES OF P OWER S ERIES Math 6B Calculus II.
1 Example 1: Find the 10 th term and the nth term for the sequence 7, 10, 13, …. Solution: U 10 = Un=Un=
Disks, Washers, and Cross Sections Review. Let R be the region in the first quadrant under the graph of c)Setup but do not evaluate the integral necessary.
Index FAQ Power Series Definition of Power Series Convergence of Power Series Generating Function for Fibonacci Numbers Radius of Convergence Finding Power.
MA.912.G.6.6: Given the center and the radius, find the equation of a circle in the coordinate plane or given the equation of a circle in center-radius.
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