题目
题目

MTH1030 -1035 - S1 2025 MTH1030/35 Week 9 lesson quiz: Representing functions by infinite series

简答题

Let’s say \[1+2x+3x^2+4^3x^3\] are the first 4 terms of the Maclaurin series of some function \(f(x)\). What is \(f’’(0)\)?

查看解析

查看解析

标准答案
Please login to view
思路分析
To tackle this, recall the Maclaurin series expansion of a function f around 0: f(x) = f(0) + f'(0)x/1! + f''(0)x^2/2! + f'''(0)x^3/3! + ... . The p......Login to view full explanation

登录即可查看完整答案

我们收录了全球超50000道考试原题与详细解析,现在登录,立即获得答案。

类似问题

Question text 9Marks a) The Maclaurin series of [math: f(x)=2cos⁡(x)]f(x) = 2\cos(x) is [math: f(x)=]Answer 1[input][math: +]Answer 2[input][math: x+]Answer 3[input][math: x2+⋯]x^2+\cdotsb) The Maclaurin series of [math: g(x)=6ln⁡(1−x)]g(x) = 6\ln(1-x) is [math: g(x)=]Answer 4[input][math: +]Answer 5[input][math: x+]Answer 6[input][math: x2+⋯]x^2+\cdotsc) The Maclaurin series of [math: h(x)=2cos⁡(3x)+6ln⁡(1−x2)]h(x) = 2\cos(3x) + 6\ln(1-x^2) is[math: h(x)=]Answer 7[input][math: +]Answer 8[input][math: x+]Answer 9[input][math: x2+⋯]x^2+\cdotsPlease answer all parts of the question.Notes Report question issue Question 7 Notes

Question text 9Marks a) The Maclaurin series of [math: f(x)=2cos⁡(x)]f(x) = 2\cos(x) is [math: f(x)=]Answer 1[input][math: +]Answer 2[input][math: x+]Answer 3[input][math: x2+⋯]x^2+\cdotsb) The Maclaurin series of [math: g(x)=6ln⁡(1−x)]g(x) = 6\ln(1-x) is [math: g(x)=]Answer 4[input][math: +]Answer 5[input][math: x+]Answer 6[input][math: x2+⋯]x^2+\cdotsc) The Maclaurin series of [math: h(x)=2cos⁡(3x)+6ln⁡(1−x2)]h(x) = 2\cos(3x) + 6\ln(1-x^2) is[math: h(x)=]Answer 7[input][math: +]Answer 8[input][math: x+]Answer 9[input][math: x2+⋯]x^2+\cdotsNotes Report question issue Question 7 Notes

Question texta) The Maclaurin series of [math: ex2]e^{x^2} is [math: ex2=]e^{x^2} =Answer 1 Question 9[input] [math: +] Answer 2 Question 9[input][math: x] [math: +] Answer 3 Question 9[input][math: x2]x^2 [math: +] Answer 4 Question 9[input][math: x3]x^3 [math: +…]+\ldotsb) The Maclaurin series of [math: ∫0x6ln⁡(1+t)sin⁡(t)dt]\int_0^x 6\ln(1+t)\sin(t) dt is [math: ∫0x6ln⁡(1+t)sin⁡(t)dt=]\int_0^x 6\ln(1+t)\sin(t) dt =Answer 5 Question 9[input] [math: +] Answer 6 Question 9[input][math: x] [math: +] Answer 7 Question 9[input][math: x2]x^2 [math: +] Answer 8 Question 9[input][math: x3]x^3 [math: +…]+\ldotsPlease answer all parts of the question.

Question texta) The Maclaurin series of [math: ex2]e^{x^2} is [math: ex2=]e^{x^2} =Answer 1 Question 9[input] [math: +] Answer 2 Question 9[input][math: x] [math: +] Answer 3 Question 9[input][math: x2]x^2 [math: +] Answer 4 Question 9[input][math: x3]x^3 [math: +…]+\ldotsb) The Maclaurin series of [math: ∫0x6ln⁡(1+t)sin⁡(t)dt]\int_0^x 6\ln(1+t)\sin(t) dt is [math: ∫0x6ln⁡(1+t)sin⁡(t)dt=]\int_0^x 6\ln(1+t)\sin(t) dt =Answer 5 Question 9[input] [math: +] Answer 6 Question 9[input][math: x] [math: +] Answer 7 Question 9[input][math: x2]x^2 [math: +] Answer 8 Question 9[input][math: x3]x^3 [math: +…]+\ldots

更多留学生实用工具

加入我们，立即解锁 海量真题 与 独家解析，让复习快人一步！