natural

1. Calculus, Natural Log problem.

Hello, not having trouble with the math so far just really whats its asking for i don't see quite clearly, f(x)= ln(x)/x^2 and so f'(x)=(1-2ln(x))/x^3 The question says "Use the definition of ln(x) as an integral to show that f(x) <1xfor all x ≥ 1." now i know the...
2. Natural Logs with e

Hi. I am trying to solve for Si2 in this equation. = 0.0175 = 0.0255 I think I can use the log rule Log (ab) = Log(a) + Log(b) but I am not sure because of the (e -1)+1 portion. Help with the operational steps to solving for Si2 would be useful. I was not sure if I should post here or to...
3. Natural number

So the problem is: The numbers a, b and c fullfill, that a2+2b2=3c2. Show that (a+2b+3c)/(a+c)*((a+b)/(b+c)+(b-c)/b-a)) is a natural number. I hope someone can help me! thx
4. Proof of Predicate Logic by natural deduction

Hello everyone. I wanted to ask how can i solve this one by natural deduction. deduction Thanks in advance ...
5. Predicate Logic with Natural Deduction

f is a function symbol, R is a relation/predicate symbol. \vdash \forall x \forall y \exists z f(x,y)=z all I have so far is 1. z=z 2. f(x,y) = z assume 2. x0,y0 fresh 3. 4. 5. 6. \forall x \forall y \exists z f(x,y)=z \vdash \exists y(R(y) \rightarrow \forall x \exists x R(x))...

7. How is the sum of all natural numbers -1/12?

I'm not smart enough to understand the Riemann Hypothesis (I am a first year college student, and I think I need a stronger math background to understand how the Riemann Zeta Function works). But obviously this is unintuitive that 1+2+3+4+5...+infinity = -1/12. My first guess was that some how...
8. Inverses of Functions containing the natural logarithm

How would one approach taking the inverse of the function g(x)=x+3ln(x-2)? Can it be simplified to a rational function? Two attempts I've made: 1. Simplified to e^x=y+3(y-2) 2. Simplified to inverse y= cube root(e^(x+y)) +2
9. Natural History and one of the researchers

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10. Definite Integral Involving Natural Log

Hello! I'm having some trouble with the following integral: $\int_{4}^{9} ln(y)/(y^{1/2}) dy$ I've started by using u = ln(y) and v = ln(y^(1/2)) for integration by parts: ln(y)*ln(y^(1/2)) - $\int_{4}^{9} ln(y^{1/2}) (1/y) dy$ but I'm not sure where to go from there... any help would be...
11. Limit of Natural Log

Find the limit of ln(6-x) as x tends to 6 from the left side. My Work: ln(6-6) ln(0) = 1 However, the answer is -infinity. I find this to be true as x tends to 6 from the right as well. I don't get it.
12. n-th root of natural number

I would like to prove that: If $m,n \in \mathbb{N}$ then $\sqrt[m]{n}$ is either an integer or irrational. Here is my attempt: Suppose that $\sqrt[m]{n} \in \mathbb{Q}$. Then $\exists \; p,q \in \mathbb{Z}$ such that $$\sqrt[m]{n} = \frac{p}{q}$$ which implies that  n =...
13. Partial derivative of natural logs

Find the partial derivatives of the following function: Q=(1/3)logeL+(2/3)logeK Any help would be much appreciated! Below is my working out so far: \frac{\partial Q}{\partial L}= \frac{\frac{1}{3}}{L} \frac{\partial Q}{\partial K}= \frac{\frac{2}{3}}{L} Are all these correct?
14. Natural Number Question.

I'm a natural number written with 10 different digits such that for all i∈1,...,10 the number formed by my i first digits (from left to right) is divisible by i. Who am I? Anyone got any insight?
15. Natural logs and solving for X

I have to following problem but it seems the answer I have does not seem correct, can someone verify and perhaps point me to any potential issues ? Thank you. 3y + ln(x) = 2 ln(4y-1) I will just do each step I did to get my answer. 3y + ln(x) = ln(4y-1)^2 3y + ln(x) = ln(16y^2+1) ln(x) =...
16. Natural logarithm-

Just checking over my assignment- i think i have most of the equation but can't work out if the last bit is correct, and if i made an error. Question: ln8+lnb-ln4=ln3 Im under the impression that the first section automatically goes to ln8^b Thus giving me.....ln8^b - ln4=ln3 Then...
17. Natural deduction, need help.

Hey, I've got to solve 3 natural deduction problems so I came here for help. 1) p => q v r premise ~q premise p v q premise r conclusion 2) p v q premise r v s premise (((p & r) v (p v s)) v ((q v r) & (q v s))) conclusion 3)...
18. 5 Steps to Increase Mass With Natural Body Building

If you are lacking clarity on a specific thing, look at it again or ask a trusted source for assistance. Allowing small problems to get in your way is really a major mistake. has been great for other people who have been in your position and needed help broadening their knowledge bases.Both Maxx...
19. Help !! Natural log of Derivative in sine

u(x) = x^(1/2) ．[Acos(CInx) + Bsin(CInx)] find u'(x). (A,B,C are constants)
20. SAT-solving: natural language -> Boolean formula -> CNF -> SAT-solver -> solution

Convert the following formula to CNF (it means, find a logically equivalent set of clauses): ((NOT x) OR y) -> (z -> x)