In Exercises 35-40, use Eq. (2) to expand the function in a power series with center c=0 and determine the interval o f convergence.$$ f ( x ) = \frac { 1 } { 1 - 3 x } $$ 相关知识点: 试题来源: 解析 3^nxn} on the interral(- $$ \frac{1}{3} $$, $$ \frac{1...
Power Series; Binomial Expansion: We'll change the function {eq}{{5} \over {(4 + x)^3}} {/eq} into the equivalent form {eq}\frac{{5}}{4^3} \left(1 + \frac{x}{4}\right)^{-3} {/eq} so that we can use the Binomial series ...
Use the binomial series to expand the function as a power series. {eq}f(x) = \frac{9}{(4+x)^3}{/eq} Power Series: Any polynomial can easily be expressed as a power series. For example, The power series of {eq}\sin(x)=x-\frac{x^3}{3!}+\frac{x^...
把一篇短篇小说扩写成一部长篇小说 to expand a phrase into a sentence 把词组扩充成句子 把(缩略式、方程式等)全部写出: 例句: to expand an equation 展开方程式 【数学】 重写(算式)以显示因数的乘积 重写(算式)表示出和、积等特殊项 展开: 例句: to expand a function in a power series©...
to expand a function in a power series. verb (used without object) to increase or grow in extent, bulk, scope, etc.: Most metals expand with heat. The mind expands with experience. to spread out; unfold; develop: The buds had not yet expanded. ...
Using the binomial series to expand √1 + as a power series as in Example 9, we get√(1+x)=(1+x)^(1/2)=1+x/2+∑_(n=2)^∞((-1)^n-1_1)/n⋅3⋅5⋅⋯⋅(2n-3)^n⋯^ 2n. n!,SO-(1-x^2)^(1/2)=1-1/2x^2-∑_(n=1)^∞(1⋅3⋅5⋅⋯⋅2n-3...
to rewrite (a mathematical expression) as a sum, product, etc., of terms of a particular kind:to expand a function in a power series. v.i. to increase or grow in extent, bulk, scope, etc.:Most metals expand with heat. The mind expands with experience. ...
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( z) in R in terms of a power series θ( t) = tq( t), where q( t) is any regular function and t is equal to the quadratic function [( z z 1)( z z 2)] , z 1 ≠ z 2, where z 1 and z 2 are two points in R and the region of validity of this formula is also ...
Using Bullet Points ( • ) Homophones, Homographs, and Homonyms Words You Always Have to Look Up Democracy or Republic: What's the difference? Popular in Wordplay See More Top 12 Sophisticated Compliments 'Za' and 9 Other Words to Help You Win at SCRABBLE ...