Hey guys, not touched any mathematics in almost 5 years and I am just getting back into it, been going well so far but hit a hurdle with this, I presume its some gaps in my knowledge.
So been at this for about an hour, got the first one, no clue on the second, can anyone offer assistance?K(-2...
Homework Statement
Let f(x) = x3ln(1+x2), and let the summation (from n=0 to infinity) anxn be the Taylor series for f about 0. Then what is a3?
Homework Equations
The Attempt at a Solution
What?! I definitely don't expect the answer, but does anyone know how I could go about...
Homework Statement
find Taylor polynomial for ln x of degree n, at 2
(Pn,2(x))
Homework Equations
Pn,1(x)= (x-1) - (x-1)2/2 + ... + (-1)n-1(x-1)n/n
The Attempt at a Solution
there doesn't seem to be an obvious pattern to this. the coefficients for n=1 to n=4 are 2, -8, 24, -64...
Homework Statement
what is the time derivative of the following expression: ln(\frac{ct+\sqrt{(c^2t^2-s^2)}}{s})
Homework Equations
\frac{d}{dx} ln x = \frac{1}{x}
chain rule
log rules eg ln (x/y) = ln x - ln y
The Attempt at a Solution
ln(ct+\sqrt{(c^2t^2 -s^2)})-ln...
Homework Statement
Let f(x) = ex + ln x
Find (f-1) ' (e)
Homework Equations
let y = f-1 x
The Attempt at a Solution
I tried finding the inverse of f(x) but got stuck. I arrived at:
x = ey + ln y
How do I make y the subject of formula?
Homework Statement
How do I calculate the variance of
\frac{1}{\log{X} + 2}
where X is a random variable?
The Attempt at a Solution
Is it:
\frac{1}{\log{var(X)}}
Homework Equations
The Attempt at a Solution
Homework Statement
Determine f^{-1}(0) of f(x) = ln (4-7x) + ln(-7-5x)
Homework Equations
f(x) = ln (4-7x) + ln(-7-5x)The Attempt at a Solution
What I did was
y = ln (4-7x)(-7-5x)
Then I swapped x and y to attempt to make the inverse function
x = ln (4-7y)(-7-5y)
and I start to solve...
Is there an easy way to change your y-variable in Gnuplot to ln y without changing the source data file?
I already tried "set log y" but that only changed the y-axis scale, not the actual y-values.
Right now I'm plotting an exponential decay and I wanted to make it a linear graph (lny vs...
the question is: differentiate wiith repsect to x:
(ln(5x))^1/5
i differentiated and got :
1/5ln(5x)
y'=1/5x
I don't think this is correct. The answer should be ln5/5.
Can anyone help me?
chanella
Homework Statement
lim(x→∞)(lnx)^2/x
Homework Equations
The Attempt at a Solution
Since lim(x→∞)(lnx )^2=∞ and lim(x→∞)x=∞, the function is indeterminate, ∞/∞.
lim(x→∞)(lnx)^2/x=lim(x→∞) d/dx (lnx )^2/(d/dx x)=lim(x→∞)(2 lnx (1/x))/1
An I am stuck...
Homework Statement
y=8^0.01x
Differentiates to: 0.01 ln8 x 8^0.01x
Using derive on a graphics calculator, the answer given is:
3x2^3x-200/100 ln2/25
Prove that the two equal each other using index and logarithm laws.
Homework Equations
The Attempt at a Solution
Ah, well...
Hi,
I start with arctanh\left(\frac{A}{\sqrt{A^2-1}}\right)=\frac{1}{2}ln\left( \frac{1+\frac{A}{\sqrt{A^2-1}}}{1-\frac{A}{\sqrt{A^2-1}}}\right)
The function \frac{A}{\sqrt{A^2-1}} is real, and since A>1, it too is always greater than 1.
Is it true that it should really be the modulus...
I get confused when it is 'ok' to use the natural logarithm when integrating a function. As soon as I see a denominator, I am always tempted to simply go 'ln(denominator)/d denominator)' but this is clearly wrong...
Is it wrong in situations where you have a polynomial denominator? For...
Homework Statement
I'm trying to understand how they got du in this problem. It is an integration by parts question. Anyway, the question asks me to evaluation this integral by using integration by parts two times
Homework Equations
This is how we would solve the problem...
Homework Statement
I've been going through a book called "Short Calculus: The Original Edition of A First Course in Calculus," by Serge Lang. It says, " The derivative of a^x is a^x (log a)." But everything else I look at says the derivative of a^x is a^x (ln a). Since ln a and log a are...
Homework Statement
2/(x lnx^2) = 1 / (x ln x)
That is the answer in the back of my textbook. I have reached 2 ( x ln x^2) , but I do not know why it is = to 1 / ( x ln x )
Homework Equations
The Attempt at a Solution
I tried to look into precal book to see if I could find...
Homework Statement
I'm doing a physics lab and need to do the uncertainties, and the method I'm using is the natural log method, hich goes like this:
(equation used was k*(x^a)*(y^b)*(z^c) )
http://img297.imageshack.us/img297/3663/lnform.jpg
The equation I'm doing...
Homework Statement
Find dy/dx of y=1/xlnx
Homework Equations
I thought that I'd have to use the quotient rule:
y'=vu'-uv'/v^2
However the differential of 1 is 0, so is this the right rule to use?
The Attempt at a Solution
u=1
u'=0
v=xlnx
v'=1/x
y'=vu'-uv'/v^2...
Homework Statement
Find lim_{n \rightarrow \infty} \sqrt[n]{n ln(n)}.
Do not use L'Hospital's Rule or Taylor Series.
Homework Equations
The Attempt at a Solution
I suspect I need to set up some inequality for this and then apply Squeeze Theorem. But I can't find any inequality...
1. Plot f(x)=5+ln(-2x+3), and its inverse.
2. I know the inverse of ln(x) is exp(1)^(x)., and to find the inverse of a function, solve for x then swap the x and y.
3. y=5+ln(-2x+3)
y-5=ln(-2x+3)
exp(1)^(y-5)=(-2x+3)
(-1/2)*[exp(1)^(y-5)-3]=x...
Can somebody show a step by step process of how to get this answer?
I keep getting -∞ when it should be ∞
heres my work:
lim x→∞ (x - ln x) = lim x→∞ ((1 - 1/x ln x) / (1/x)
then apply l'hospitals rule
lim x→∞ (x^(-2) ln x - x^(-2)) / (-x^(-2))
then I cancel all the x^(-2) and...
Homework Statement
hey guys, got a question. how do you differentiate y=ln(1+x^2)^1/2. any help would be appreciated, thanks
Homework Equations
answer is x/(1+x^2)
The Attempt at a Solution
hello,
I was trying to figure out what will be the y value for this equations:
1 - e^-0.15*10^-5*y = 0.1
Could somebody help me in this?? The answer is supposed to be 70,240.
thanks.
Homework Statement
lim as x approaches 0 of (x + 1)ln x
Homework Equations
The Attempt at a Solution
I tried using ln y = (ln x)[ln (x + 1)]
then:
ln (x + 1)
----------
1
---
ln x
to make it eligible for L'Hopital's Rule. Then differentiating the numerator and the denominator, I got:
1
---
x...
as part of a question i need to integrate
\intln2|x|dx (from -1 to 1)
what i did was integration in parts
\intln2|x|dx =x*ln2|x| - \int2(lnx/x)xdx
=x*ln2|x| - 2[xln|x| - x]
=lim x(ln2|x|-2ln|x|+ 2)|^{-1}_{0-\epsilon} +(ln2|x|-2ln|x|+ 2)|^{0+\epsilon}_{1}
\epsilon->0
1st of...
I don't understand what is happening in the following problem.
What happens to ln when it moves to the RHS?
Why are there two exponential functions on the RHS and why is e^c made to equal A?
http://users.on.net/~rohanlal/mathproblemln.jpg
Homework Statement
Differentiate the following:
y = ln(2x^2 - 2) / x^2 - 1
The Attempt at a Solution
The answer is y' = -ln(2x^2 - 2)(2x)(x^2 - 1)^-2 + 4x / 2x^2 - 2 (x^2 - 1)^-1
I understand all of it except 4x / 2x^2 - 2, how does ln(2x^2 - 2) derive into 4x / 2x^2 - 2?
Homework Statement
http://img5.imageshack.us/img5/2327/nummer1.jpg
Homework Equations
5a: ln((x*(x-2))/(x2-4))
ln((x22x)/(x2-4))
ln(x/(x+2)) <-- the answer (i think)
The Attempt at a Solution
Im not completely sure about that answer in 5a so could somebody check...
Homework Statement
http://img16.imageshack.us/img16/2327/nummer1.jpg
Homework Equations
Sn=(u1(rn-1))/(r-1)
The Attempt at a Solution
I think i need to use the equation for geometric series(above). Or do i use the arithmetic furmula since ln(a/b)=ln(a)-ln(b). I think i am a bit...
find the solution of this ln equation:
ax=lnx
i tried:
e^{(ax)}=x
e^{(ax)}-x=0
what to do next??
i thought of building a taylor series around 0 for ln
but ln(0) is undefined
??
Homework Statement
If a differentiable function f(x) satisfies the equation f(xy) = f(x) + f(y), prove then that f(x) = alnx.
Homework Equations
The Attempt at a Solution
I have proved that if f satisfies f(x + y) = f(x)f(y) then f(x) = 0 or f(x) = e^(ax)
and I also know that...
I am completely at a loss with this question :confused:
If one assumes that the current growth rate of consumption remains constant, the then expiration time in years is give by: T=1/r ln (rR/C + 1) where C = current consumption, r = current growth rate of consumption, and R = resource size...
In calc we are having like this flash card quiz and you have to apply things to the graph of like e^x or lnx.
I was wondering how do you determine the domain range of graphs like these.
for example e^x graph domain is all reals, and the range is 0 to infinity. How would you transform this...
I have tried quite a few methods but haven't solved this problem, any help ?
\oint axLn(x/b) dx
where a and b are constants
I have tried moving the 'a' outside the integration and solving xln(x/b) using integration by parts . I have also tried splitting xln(x/b) into xlnx -xlnb and...
Homework Statement
I'm taking a math of investment and credit course, in this case, solving for i which is the interest rate.
My question is: is it possible to "ln both sides" of an equation? Like in (b) below, I know I could say y*ln(1+i) = ln(3).
Homework Equations
(a) 5(1+i)^8 +...
Homework Statement
limit x --> infinity, (1+ [(ln2)/x])^x
Homework Equations
The Attempt at a Solution
I tried raising the whole thing to e ln [function] so that the x power would get eliminated. What I've got right now is this:
e lim(x->infinity) ln([x+ln2]/2)^x
e...
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)...
1. lnx + ln(x+2) = ln3
2. just work the problem out using distributive property
[b]3.
ln2x = ln3-ln2
ln2x = .4054/b]
ehh..I am just doing this one wrong. It is hard to believe what summer vacation can do to you :redface:
I have to sketch the following function:
y=x(lnx)^3
The ln scares me a bit... I have found the derivative of the function as 3(lnx)^2, and when making that equal to zero I got an anwer of around 0.7 if i remember correctly. This I guess is my critical number? Then the second derivative is...
Homework Statement
Find
\int ln x^{2009}
Homework Equations
The integration by parts!
The Attempt at a Solution
I have been trying to discover a series which might have helped:
I have taken out the integrals of :
1) ln x = x ln x -x
2) ln x^{2}=x (ln x^{2})-2x ln x +2x
3)ln...
hi, I'm new around here but i really need your help this question is similar to one already solved here some years ago
so my problem is:
1.The vapour pressure of benzene between 10°C and 30°C fits the
expression log(p/Torr) = 7.960 - 1780/(T/K). Calculate (a) the enthalpy of...