Deriving ln(x) series - Physics Forums
2007年12月9日 · How do you go about deriving the series expansion of ln(x)? 0 < x I got the representation at math.com but i'd still like to know how they got it. It's been a while since i did calc. iii. Thanks. John
The limit as x approaches 1 of x / ln (x) - Physics Forums
2008年9月6日 · Homework Statement Hi. I'm having problems with the limit of x --> 1 of ( x / ln(x) ). Homework Equations L'Hopital's Rule Algebraic Manipulation The Attempt at a Solution I understand that the the limit will give me a semi-indeterminate form (that is, it's answer is 1 / 0)...
How do you find the first and second derivative of #(lnx)/x^2#?
Let's rewrite #lnx/x^2# as #x^-2lnx.# If we have a positive exponent in the denominator, we can move the term up to the numerator and in turn make the exponent negative. It's nice to avoid using the Quotient Rule where unnecessary.
How do you find the derivative of ln x? - Socratic
2015年4月18日 · The "how" depends on the definition you are using for #lnx#. I like: # lnx = int_1^x 1/t dt# and the result is immediate useing the Fundamental Theorem of Calculus . If you start with a definition of #e^x# and find its derivative, then you probably defined #lnx# by:
Reduction formula for ∫(lnx)^n dx - Physics Forums
2010年10月24日 · Homework Statement derive a reduction formula for ∫(lnx)n dx and use it to evaluate ∫1e (lnx)3dx Homework Equations The Attempt at a Solution In other examples we've started by saying ∫(lnx)ndx = ∫(lnx)(lnx)n-1dx and using integration by parts. So let: f …
What is the limit of x^lnx as x approaches 0+? - Physics Forums
2012年1月22日 · Well, I know that e^ln(x^lnx) is the same as x^lnx, but I put aside the e for the end of the equation. ln(x^lnx)= lnx*lnx. To apply L'Hospitals Rule I have to have it in quotient form, so I rearranged my equation to lnx/ (1/lnx). After taking the derivative of both I ended up at …
What is the integral 1/x log(x) or lnx? - Physics Forums
2011年10月26日 · What is the integral 1/x log(x) or lnx? Thread starter pb23me; Start date Oct 26, 2011; Tags Integral Oct ...
Find x for ln x=-2 using the natural logarithm formula - Physics …
2010年10月8日 · No, I'm not saying that at all. For the real number version of the ln function, the domain is positive real numbers, and the range is all real numbers.
Does ln[ln(x)] = ln(x) * ln(x) - Physics Forums
2010年1月23日 · Homework Statement Does ln[ln(x) = ln(x) times ln(x)? Homework Equations The Attempt at a Solution
How to prove ln(x) < sqrt(x) for all x>0 - Physics Forums
2010年9月27日 · Hi, I know I can use a graphical calculator to easily show that How to prove ln(x) < sqrt(x) for all x>0 But I wonder if there is a rigorous way to demonstrate this.