结果1 题目 Show that the Maclaurin series for ln (1+x) is x- (x^2)2+ (x^3)3-⋯ + ((-1)^(n+1)x^n)n+⋯ . This series is valid for -1 x≤ 1 only; by drawing graphs of y=ln (1+x) and several successive approximations show that this is plausible. (This ...
常见的麦克劳伦极数公式General Maclaurin Series
常见的麦克劳伦极数公式General Maclaurin Series
In the Maclaurin expansion series, this looks like this: {eq}f(x)=f(0)+f'(0)(x-0)+\dfrac{f"(0)}{2!}(x-0)^{2}+\dfrac{f^3(0)}{3!}(x-0)^3 {/eq}. This creates a Maclaurin polynomial which estimates the original function at the point where x=0. The greater the ...
FindtheMaclaurinseriesforthefunctions Step1.ConstructingtheMaclaurinseries,obtain theintervalofconvergence. fx 0 0 ! n n n f x n 0 0 ,. ! n n n f xxI n lim0 n n Rx Step3.Drawaconclusion. Step2.AnalysisthelimitoftheRemainder. 目录上页下页返回结束 Example5. Solution. ,.x 0.cx ...
- x^7/7! +... List the terms for ln(1+x) x - x^2/2 + x^3/3 - x^4/4 +... What is the radius of convergence for 1/1-x R =1 What is the radius of convergence for e^x R= infinity What is the radius of convergence for sinx ...
Example 2 Find the 5th-degree Taylor polynomial centered at 0 for cos x. Show Answer Example 3 What is the Maclaurin series for f(x) = cos x (a.k.a. the Taylor series for f(x) = cos x near x = 0) ? Show Answer Example 4 What is the nth term, or general term, of ...
Find the Maclaurin series for f(x). f(x)=ln(1−3x). Finding the Maclaurin Series: We can define the Maclaurin Series as f(x)=f(0)+f′(0)x+f″(0)2!x2+f‴(0)3!x3+f⁗(0)4!x4+... centered at a=0. For writing this series, we require the derivatives of the ...
麦克劳林级数(Maclaurin series)是函数在x=0处的泰勒级数,它是牛顿(I.Newton)的学生麦克劳林(C.Maclaurin)于1742年给出的,用来证明局部极值的充分条件,他自己说明这是泰勒级数的特例,但后人却加了麦克劳林级数这个名称 长图 û收藏 转发 评论 ñ赞 评论 o p 同时转发到我的微博 按热度...
Find the first three terms of the Maclaurin series representation of the function f(x) = e^(-x). Find the first four terms of the Maclaurin series for the functions. a. e^x \sec x \ b. x^2 \ln(2 + x) Compute the first four terms, (n = 0, 1, 2,...