1. G

    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. A

    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. H

    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. T

    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. F

    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))...
  6. N

    Find natural number xyz

    I tried to write this one in tex without success, sorry about this. Please help me solve this problem. You need to find natural number xyz (3 digits) with: Thank you
  7. T

    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. M

    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. J

    Natural History and one of the researchers

    Bears vs Chiefs Live Streaming
  10. C

    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. R

    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. I

    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. Mr Rayon

    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. S

    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. M

    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. D

    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. X

    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. B

    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. C

    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. B

    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)