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Mar 6, 2007 · The discussion centers on the validity of the expression ln (-1) = 0, with participants noting that the natural logarithm is not defined for negative real numbers. While some argue that ln (-1) can be ex...
Feb 23, 2006 · The discussion revolves around developing the Taylor expansion for ln (1+z). Participants express confusion about the problem's wording and the appropriate point of expansion, with suggestions to use z=...
Jan 31, 2011 · The discussion explores the relationship between the natural logarithm of the imaginary unit i and the mathematical constant pi, revealing that ln (i) equals (1/2)pi*i. Participants note that the comple...
Mar 20, 2007 · The discussion centers on the correct interpretation of the natural logarithm of pressure (ln (p)) in the context of a vapor pressure experiment. It clarifies that ln (p) should be treated as dimensionl...
Jan 4, 2019 · To illustrate this further, if we somehow experimentally determined the ln k and 1/t (appears very often in our homework), we usually start by graphing them. The linear regression is seen (using Arrheniu...
Sep 14, 2018 · Homework Statement Find the sum of ∑ n = 2 ∞ ln (1 − 1 n 2) Homework Equations No one. The Attempt at a Solution At first I though it as a telescopic serie: But it doesn't look like so. we know from it'...
May 19, 2010 · Find the Maclaurin series for the derivative of ln (1+x^3), by using the geometric series.
Jul 4, 2010 · The equation e^ln (2) = 2 is derived from the properties of inverse functions, specifically how exponentiation and logarithms relate to each other. Taking the natural logarithm of both sides reveals that...
Jul 23, 2010 · Arctanhy is defined to be the number x such that tanh (x)=y. So to prove that arcanh (y)= (1/2) ln ( 1+y / 1-y ), it's the same thing as showing that tanh ( (1/2) ln ( 1+y / 1-y ))=y
Jan 13, 2005 · The discussion focuses on proving that the limit as n approaches infinity of (1 + 1/n)^n equals e, which is defined as the unique number satisfying the derivative condition of e^h at h=0. Participants s...
