Natural log Definition and 147 Threads

Homework Statement Find the sum of the series, if it converges, of n=1 to infinity of ln(n/(n+1)) The Attempt at a Solution My intuition tells me the series converges because as n goes to infinity the series is taking the log of 1, which is 0. How to sum it though... I have no...

Homework Statement [Intgrl]ln(x^(2)+4)dxHomework Equations [Intgrl]udv=uv-[Intgrl]vduThe Attempt at a Solution [Intgrl]ln(x^(2)+4)dx, u=ln(x^(2)+4), du=(2x/x^(2)+4), dv=dx, v=x xln(x^(2)+4)-[Intgrl](2x^(2)/(x^(2)+4))dx

Title says all.

Homework Statement How would I begin to integrate ln(t+1) from 0 to e^2x? Homework Equations d/dx[log base a of u]=1/(lna)u du/dx Can the original equation be manipulated to use this derivative? The Attempt at a Solution Not sure where to start.

Hey all. I'm having some problems with the partial derivatives of e. I understand the basics such as exy2. where I'm getting confused is with the following dz/dx=e(x+y) and dz/dx=1/ex+ey Can anyone help me out with understanding these??

Homework Statement We're doing a lab and we basically had to find ln(Pv), where Pv is vapor pressure of isopropanol. Well, the pressure is initially measured in kPa, but what happens to the units if you take a natural log of that whole thing? For example, if I take ln(5 kPa), do the units...

Integrating Natural Log Function using "Integration by Parts" Method Homework Statement The problem says to integrate ln(2x+1)dx Homework Equations I used u=ln(2x+1); du = 2dx/(2x+1); dv=dx; v=x The Attempt at a Solution So, I integrated it using that (above) 'dictionary' and I...

Homework Statement F(x) = (8-12ln|x|)/(x^4) > 0 (a) For what values of x is the expression F(x) defined? Write your answer in interval notation. (b) At what value(s) of x is the expression F(x) equal to zero? If there is more than one answer separate them by commas. (c) The set of...

Integrate the function. (3x)/(3x-2) I am spose to use integration by parts but i don't know how to integrate 1/(3x-2). anybody help??

I hit the submit instead of the preview. please wait Homework Statement \int9s9^s dsHomework Equations ∫udv=uv-∫9^sds-∫vduThe Attempt at a Solution u=9s du=9ds dv=9^s ds v=∫9^sds =∫3^(2s) ds =3^(2s)/[2ln(3)] this is as far as i have gotten. Am i correct so far?

how the heck do you simplify this ? (Ln (2x/y) / Ln (x/y)) = m/n HELP ME!

I am starting my first year of college and I reviewing my high school notes from trig pre-cal and there was one thing I couldn't figure out. It was a multiple choice question and I don't have the textbook anymore but the answer I circled I can't understand how I arrived to that answer...

Homework Statement sqrt(ln(x)) = ln(sqrt(x)) Homework Equations The Attempt at a Solution I've been trying to do this for some time now. Could anyone give some tips on how to get started with this?

Is it true that e^{2(2x+ln2)} = e^{4x}e^{2ln2} I can't see how that is true? According to a paper mark scheme it is. Can someone clarify Thanks :)

Homework Statement The function f(x) =ln(10 - x) is represented as a power series in the form f(x) = (sum from 0 to infinity) of c_{n}x^{n} Find the first few coefficients in the power series. The Attempt at a Solution I know how to find the coefficients in a normal looking...

i need help with this: lim x->\infty of \frac{ln(2+h) - ln(2)}{h} i have no idea where to even begin! i tried resolving it, but it didn't help :[ any suggestions??

y''-y'-30y=ln(t) My attempt: i tried to use the method of undetermined coefficients. y''-y'-30y=ln(t) Y(t)=A lnt Y'(t)=A/t Y''(t)= -A/t^2 I also tried: Y(t) = A ln(t) + B 1/t + C 1/t^2 now I am stuck...any help??

Homework Statement Find the limit of (tanx)^cosx as x-->infinity Rearrange the equation so that you can use L'Hopital's rule for the form of (infinity/infinity) The Attempt at a Solution I did ln(tanx)^cosx = cosxlntanx I know the limit of tanx as x-->infinity is pi/2 the limit of cosx as...

I've got a simple question that's been bugging me for a while. I think I know where the problem is, I'd just like a formal mathematical reason why I can't say this: \ln{(-1)}^2 = \ln(1) = 0 That part is fine...but then: \ln{(-1)}^2 = 2 \ln(-1) = 2 (i \pi) when they should...

Homework Statement Let f be the function given by f(x) = ln [ x/ (x-1)] (a) What is the domain of f? (b) What is the value of the derivative of f at x = -1. (c) Write an expression for f^(-1) of x, where f^(-1) denotes the inverse function of f. The Attempt at a Solution a. x / x-1...

can someone please explain this to me?

Homework Statement Find y' y=ln(x^2 + y^2) Homework Equations d/dx ln(u)= 1/u du/dx The Attempt at a Solution y' = [1/(x^2 + y^2)] (2x + 2y) y' = (2x+2y)/(x^2 + y^2) But my book says the answer is 2x/(x^2 + y^2 - 2y) How can that be?

Problem: If 2^{x}=3, what does 3^x equal? I solved this by taking the log_{2} of both sides. However, the book's solution involves taking the natural log of both sides. Can someone show me why that would work? I don't get what the x power changes to a x term. The natural log is base 10 right?

I'm having real problems integrating a natural log. The problem I have been set is (where S = integration sign) S (x - 2) Ln(3x) I'm trying to use the integration by parts rule but keep getting the wrong answer and I think it might be to do with the natural log. I have used f(x) =...

If we have a function of the form Ln(ax) Is it the case that the derivative is simply 1/x no matter what the initial value of 'a' might be? Or do we take into account 'a' in some way The thing i need clarifying is this... If we have Ln(3x), the derivative is 1/x, but the integral of...

Homework Statement the indefinite integral of (1+lnx)^(1/2)/(xlnx) dx Homework Equations n/a The Attempt at a Solution There aren't any x^2 in the root sign, so I don't think it can be a trig substitution. The only logical u sub I see is to let u=lnx. In that case, du=dx/x so the...

I was working on an experiment for the vapor pressure of water and I have the following formula ln (p) = -L/(RT) + ln (p_o) L=heat of vaporization of water R=Molar gas constant T=temperature in Kelvins I have some data points for the pressure p in units of mm Hg, when I take the...

Can someone explain to me when to use natural log or common log? I understand that natural log gives creates a base e and the common base 10 but i don't understand why there are 2 different ones.

Homework Statement find dy/dx for y=ln(sec^(2)x) Homework Equations none The Attempt at a Solution 1.)1/(sec(x)^2)*dy/dx sec(x)^2 2.)tan(x)/sec(x)^2 3.)i put it in terms of sin and cos... sin(x)/cos(x)*cos(x)^2/1 4.)i canceled the cos(x) in the denominator and came...

I have the problem 3e^(x+2) = e^(-x) and I need to find X. It's been a while since I've looked at any Calculus 2 stuff so I am not sure on what to do here. I take the natural log of both sides LN(3e^(x+2) =LN(e^(-x))= (x+2)ln3e = -xlne So (x+2)Ln3e= -x Where do I go from here?

Having some trouble understanding derivatives including numbers to the "X" power. For example, f(x)= 7^8^x, f'(x)=? help please!

Find the first derivitive. Simplify if possible (factor). \begin{array}{l} y = x^{e^x } \\ \\ \ln y = \ln x^{e^x } \\ \\ \ln y = e^x \ln x \\ \end{array} There's a similar problem in my class notes where it was solved by taking the natural log of both sides. Is this...

this problem is an excerpt from an explanation of a time wieghted performance method. I feel that if I can follow this part the rest of it will make sense. now i know the answer is .1259 but I'm a little fuzzy on how exactly they got that, and their 'step by step' seems to miss some steps. it...

Hello everyone the problem I am messing up is: . Solve the following initial value problem: http://img59.imageshack.us/img59/9037/lastscan4vl.jpg When pluggin in answers and using my calculator to evaluate, its saying NON-REAL numbers, I'm messing up hardcore somewhere but not sure where...

Problem states: (A) Use mathematical induction to prove that for x\geq0 and any positive integer n. e^x\geq1+x+\frac{x^2}{2!}+...+\frac{x^n}{n!} (B) Use part (A) to show that e>2.7. (C) Use part (A) to show that \lim_{x\rightarrow\infty} \frac{e^x}{x^k} =...

I have a tricky natural log in front of me. It's ln(1/x). The reason it's tricky is because I thought that I could re-write it as ln(1)-ln(x), as per the rules of logs, but that doesn't seem to agree with my calculator. Is there a reason why? Thanks!

Hi all. I'm slightly confused with the following limit prob: \lim_{x\rightarrow \infty} \frac{(ln (x))^n}{x} which I know = 0. (n is a positive integer) It looks like it's of indeterminate form, that is \frac{\infty}{\infty} Using L'Hopital's, it looks like you get another indeterminate form...

when trying to solve ln(x+4)=2 i tried this ln(x+4)=2 e^2=(x+4) ln e^2=ln(x+4) 2=ln(x+4) and round and round i go... where do i start to go wrong?

Hello all. I am stuck on this homework problem. It wants me to find \frac {d^2y} {dx^2} when y= ln x^8 The book answer is \frac {-8}{x^2} But I only can get \frac {-8}{x^9)} Please give me some guidance Thanks

Ok so i was doing a problem involving finding the pressure of mercury at its boiling point (630.05K) using Troutons rule and the final answer seems a bit strange to me. Integration of the Clausius-Clapeyron Equation: {ln(\frac{{P}_{2}}{{P}_{1}}) =...

Hello all If y = e^3^\ln^(x^2) find \frac {dy}{dx} So \frac {dy}{dx} =(3 (\frac {1}{x^2}) \* 2x e^3^\ln^(x^2) So the simplified answer is: \frac {6}{x} e^3^\ln^(x^2) Is this correct? IS there any other way of expressing the answer? Thanks

Hi everyone! (d/dx) [xlnx] Why is the answer 1+lnx and not 1?? ~Thanks

Please Help! Natural Log Question! Here is the question that is bothering me: I need to solve this natural log for x. Please I need step by step instructions on how to figure out x. Thanks very much. ln (x) + ln (x+1) = 2

Here's the problem: find the integral of dx/2x(lnx)^1/2 In other words, dx over 2x times the square root of lnx. It has to be evaluated from 16 and 2. I don't know how to say it, but the integral sign with 16 at the top, and 2 at the bottom. If you can find the answerm and show me...

[SOLVED] Integration of a natural log I am asked to Integrate by parts \int \ln(2x+1) dx So, \mbox{u}=ln(2x+1) \mbox{du}=\frac{2}{2x+1} \mbox{dv}=\mbox{dx} \mbox{v}=\mbox{x} I plug all of that in and I get, {\int \ln(2x+1) dx\}={\mbox{x}\ln(2x+1)}-{\int \frac{2x}{2x+1}...

Hi, I am still having trouble with taking the integral of the following: integral of ln(x+1) dx I am trying to do it by parts but I end up getting stuck. I had no problem doing: integral of ln x dx But I can't seem to get integral of ln (x+1) dx Let u = ln (x+1) then du =...

Hello, It has been over a year since I last took calculus. And I don't recall how to take the integral of a natural logarithmic function. Here is the question that I am supposed to integrate. double integral 1/(x+y) dA where R = [1,2] X [0,1] So what I did first was integrate...