# proof

12. ### Proof of e^x, lnx and e as limit without circular dependency?

People prove the derivative of e^x, \ln(x) using either the formula of e = \lim_{x \to 0} (1+x) ^ \frac{1}{x} or if they know one of the derivatives e^x, \ln(x) they use it to prove the other. My textbook first gave me without proof that \frac{d}{dx}e^x = e^x Then it found the limit of \ln(x)...
13. ### Proof of goldbach's conjecture

PROOF OF GOLDBACHâ€™S CONJECTURE Goldbachâ€™s conjecture states that every even integer > 2 is the sum of 2 primes. An example is 100 = 3 + 97 = 11 + 89 = 17 + 83 = 29 + 71 = 41 + 59 = 47 + 53. An alternative statement of the conjecture is as follows. Every integer > 3 is the arithmetic mean of...
14. ### proof of property

Let a 3 Ã— 3 matrix A be such that for any vector of a column v âˆˆ R3 the vectors Av and v are orthogonal. Prove that At + A = 0, where At is the transposed matrix.
15. ### Help with proof?

The givens are, Quad ABCD is inscribed inside the circle Diagonals AC and BD meet at point E. Line AD is congruent to Line CD How do you prove that BE * AD = EC * AB?
16. ### Inequality proof

Prove : 1+1/2 +1/3 +....+ 1/2^{k} \geq 1+k/2. For k=0,1,2,3... .
17. ### Asymptotic Normality proof

I'd like some assistance on the proof of the following Lemma: If $X_n$ is $AN(\mu,\sigma_n^2)$, then also $X_n$ is $AN(\overline\mu,\overline\sigma_n^2)$ if and only if \frac{\overline\sigma_n}{\sigma_n}\rightarrow1, \frac{\overline\mu_n-\mu_n}{\sigma_n}\rightarrow0. The hint says to use...
18. ### Proof for natural logarithm limit without differentiation

I have another limit where I'm struggling with the solving.Can somone help me? https://ibb.co/5Kq58jR I used a method like this but I'm not 100% if it's correct! https://ibb.co/JQrpdL1 What should I do from that step? I know something like arctan(x)/x when x tends to 0 is 1. How is that...
19. ### Proof for this power limit without differentiation

https://ibb.co/WVC8BgJ I am stuck at the last step and I don't know how to go on.Can someone help me?What do I do from the last step?
20. ### proof

How can I proof (Kn, t) = t(t 1)(t 2)Â·Â·Â·(t (n 1)). number of way of coloring a complete graph (Kn) with n vertex, with palette of t colors.