Finding Taylor Series of Common Functions
Read this topicExplanations 5
- Exponential function: exe^xex Simple, right? Still keeping up? Good. Now for the important part: That wasn't a trick, it's still one. Since the nthn^{th}nth derivative of exe^xe…
By Tim Ratigan, Matt Superdock, Expii Team, Moor Xu, Alex Federspiel
- Trigonometric functions: sinx\sin xsinx and cosx\cos xcosx We will begin by finding the series for sinx\sin xsinx The first question we must tackle, which is of the utmost im…
By Tim Ratigan, Tom Shen, Expii Team, Moor Xu, Alex Federspiel
- Hyperbolic Function: 11−x\frac1{1-x}1−x1 There are several ways to find the Taylor series for this function. One way is to try to get rid of the denominator: Note that, if we m…
By Tim Ratigan, Moor Xu
- Natural Logarithm: lnx\ln xlnx We obviously cannot have a Taylor series centered at x=0x=0x=0 for f(x)=lnx,f(x) = \ln x,f(x)=lnx, so we will instead pick x=1x=1x=1 as an obvio…
By Sujay Kazi, Alex Federspiel
- e^x is 1+ x + x^2/2! + x^3/3! + .....
By Ujjawal Gupta
Problems 3
- There is a unique real number ppp such that the limit limx→∞xp(x+13+x−13−2x3)\lim_{x\to\infty} x^p(\sqrt[3]{x+1} + \sqrt[3]{x-1} - 2\sqrt[3]{x})limx→∞xp(3x+1+3x−1−23x) is a…
- Estimate 1.01\sqrt{1.01}1.01 to 444 significant figures.
- Which function does this Taylor series correspond to? x+2x22!+x33!+x55!+2x66!+x77!+…x + 2 \frac{x^2}{2!} + \frac{x^3}{3!} + \frac{x^5}{5!} + 2\frac{x^6}{6!} + \frac{x^7}{7!} + \…