# 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)