How about three things that are infinite. Counted number are infinite. The complete statement of PI is infinite. The result of 1 divided by 3 is infinite.
Compare a series to a known series. So take the harmonic series {1/1 + 1/2 + 1/3 + ... + 1/n}, which diverges.For each number n [n>1], LN(n) < n, so 1/(LN(n)) > 1/n. So since each term in 1/LN(n) is greater than each term in the divergent series {1/n}, then the series 1/LN(n) diverges.
Use the product rule.y = x lnxy' = x (ln x)' + x' (ln x) = x (1/x) + 1 ln x = 1 + ln xUse the product rule.y = x lnxy' = x (ln x)' + x' (ln x) = x (1/x) + 1 ln x = 1 + ln xUse the product rule.y = x lnxy' = x (ln x)' + x' (ln x) = x (1/x) + 1 ln x = 1 + ln xUse the product rule.y = x lnxy' = x (ln x)' + x' (ln x) = x (1/x) + 1 ln x = 1 + ln x
ln 1 = 0 e0=1
An infinite number of integers can be divided by 126.
converges to zero (I think)
x^(ln(2)/ln(x)-1)
0.5
1/ln(x)*e^(1/x) if you differentiate e^(1/x), you will get ln(x)*e^(1/x). times this by 1/ln(x) and you get you original equation. Peace
3
How about three things that are infinite. Counted number are infinite. The complete statement of PI is infinite. The result of 1 divided by 3 is infinite.
The first of an infinite series of solutions is: log10(-2.4969)=ln(-2.4969)/ln(10)=ln(2.4969)/ln(10) +PI*i/ln(10) = .397 + 1.364*i There are an infinite number of additional solutions of the form: .397 + 1.364*i +2*PI*k/ln(10) where k is any integer greater than 0. I got this number by using the change of base identity and a common, complex log identity, neither of which I'm deriving. If you haven't been taught it yet, i = sqrt(-1).
The limit is 4.
1
1 time infinity equals infinity. Infinite divided by infinite equals 1. There's your answer. * * * * * Except that it is not true. 1 times infinity is, indeed, infinity. But infinity divided by infinity need not be 1. See for example, the paradox of Hibert's Hotel at the attached link.
Compare a series to a known series. So take the harmonic series {1/1 + 1/2 + 1/3 + ... + 1/n}, which diverges.For each number n [n>1], LN(n) < n, so 1/(LN(n)) > 1/n. So since each term in 1/LN(n) is greater than each term in the divergent series {1/n}, then the series 1/LN(n) diverges.
There are an infinite number of possible answers. Amongst the simpler is 1428 divided by 1.