Calculus: concepts and contexts : single variable : release 1.1. Chapters 5-8, Volume 2Brooks/Cole Publ. Company, 1997 - 302 pages |
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Page 348
... Series 609 8.7 Taylor and Maclaurin Series 615 8.8 The Binomial Series 626 How Newton Discovered the Binomial Series 630 8.9 Applications of Taylor Polynomials 631 Applied Project : Radiation from the Stars 639 8.10 Using Series to ...
... Series 609 8.7 Taylor and Maclaurin Series 615 8.8 The Binomial Series 626 How Newton Discovered the Binomial Series 630 8.9 Applications of Taylor Polynomials 631 Applied Project : Radiation from the Stars 639 8.10 Using Series to ...
Page 627
... series . It is possible to prove this by showing that the remainder term R , ( x ) approaches 0 , but that turns out to be quite difficult . The proof outlined in Exercise 15 is ... binomial series with k = = 1 + 8.8 The Binomial Series 627.
... series . It is possible to prove this by showing that the remainder term R , ( x ) approaches 0 , but that turns out to be quite difficult . The proof outlined in Exercise 15 is ... binomial series with k = = 1 + 8.8 The Binomial Series 627.
Page 628
... Binomial Series The. A binomial series is a special case of a Taylor series . Figure 1 shows the graphs of the first three Taylor polynomials computed from the answer to Example 2 . 1 4- x + -4 and with x replaced by -x / 4 , we have - 1 ...
... Binomial Series The. A binomial series is a special case of a Taylor series . Figure 1 shows the graphs of the first three Taylor polynomials computed from the answer to Example 2 . 1 4- x + -4 and with x replaced by -x / 4 , we have - 1 ...
Common terms and phrases
Alternating Series an+1 antiderivative approximating rectangles binomial series calculator computer algebra system constant convergent or divergent cross-section decimal places defined definite integral derivative differential equation direction field distance traveled error Euler's method evaluate the integral Evaluation Theorem Example Exercise exponential Find the area Find the volume formula function f(x Fundamental Theorem ƒ is continuous geometric series given series graph of ƒ height improper integral increasing infinite initial initial-value problem interval of convergence length limit limn Maclaurin series Midpoint Rule Newton Notice partial sums population positive power series rabbits radius of convergence Ratio Test Riemann sum right endpoints Section sequence series converges shown in Figure Simpson's Rule sketch solution curve solve subintervals Suppose tank Taylor polynomial Taylor series Trapezoidal velocity x-axis УА