Write down the first three non-zero terms in the Maclaurin series for ln (1+2x), where -0.5 x≤ 0.5, simplifying the coefficients.It is given that the three terms found in part (i) are equal to the first three terms in the series expansion of ax(1+bx)^c for small x. Find the...
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 series was fi...
{eq}f(x) = \ln (1 - x^2) {/eq} Maclaurin Series: Maclaurin series allows one to calculate the approximation of a function {eq}f\left( x \right) {/eq} for input values. Let {eq}f\left( x \right) {/eq} be a function of {eq}x {/eq} then ...
Maclaurin Series for In(1+x) | Expansion, Formula & Steps from Chapter 26 / Lesson 11 68K Learn what the ln of 1 is and how the equation ln(x)=1 can be solved. Then, learn how to find the Maclaurin series for ln(1+x...
Replies: 1 Forum:Calculus T MHBHow do I find the MacLaurin series for $\frac{1}{1 - 2x}$? I need to find the maclaurin series of the function $$\frac{1}{1 - 2x}$$. I know $\frac{1}{1 - x}$ is $1 + x + x^2 + x^3 ...$ but how can I use this to solve the...
(2) f(x)=ln(1-x)=ln[1+(-x)] =(-x)-1/2(-x)^2+1/3(-x)^2-1/4(-x)^1+⋯+ (-1)^n⋅((-x)^n)/n+(-1)^n((-x)^(n+1))/((n+1)(1-θx)^(n+1)) (n+1)(1-0x)"+ x"-1 =-[x+1/2x^2+1/3x^2+⋯+(x^(n+1))/n+n/((n+1)(1-θx)^(n+...
苏格兰数学家科林·麦克劳林(ColinMaclaurin)研究出了著名开始的Maclaurin级数展开式,其中一个为:ln(1+x)=x-(x^2)/2+(x^3)/3-(x^4)/4+⋯+(-1)^(n-1)(x^n)/n+⋯ ,据此展开 N=100, i=1, S=0isN?式,右图所示的程序框图的输出结果S约为否是(参考数据: ln2.414=0.8813 , ln2=0.6931 ,...
Find the Maclaurin series for f(x) = x^9\sin(x). Find the Maclaurin series for f(x). f(x) = \frac{x}{1 - 2x^3}\f(x) = \sum_{n = 0}^\infty\boxed{\space}. Find the Maclaurin series for f(x) = x^3 \ln(1 + x) ...
1.Howaccuratelydoafunction’sTaylorpolynomial approximatethefunctiononagiveninterval? 2.Forwhatvaluesofxcanwenormallyexcepta Taylorseriestoconvergetoitsgeneratingfunction? fx n Px ? fx 0 ! n n n fa xa n ? 目录上页下页返回结束 TheRemainderandtheError Exactvalue. n fxPx n Rx fx n Px n ...
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