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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.
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What is the infinite limit of 1 divided by ln x?
The limit should be 0.
What is the derivative of y equals xlnx?
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
What does ln 1 equal?
ln 1 = 0 e0=1
Give examples of a convergent series.?
These are some series (not the summation of series) that converge: 1/n1/n2(a/b)n if a/b < 1 or = 1sin(1/n)cos(1/n)sin(nπ) π = picos([2n+1]π/2)e-n(n+2)/n
What is min minus superscript 1?
For those of us who know non-Lygerian mathematics ---- there is no unique solution but it can be approximated with the series sol = 1 + ab x + 2ab2/c3 x + 3ab3/c5 x + 4ab4/c7 x + ..... where x is either -ln(min) or +ln(min)
What is 2 divided by x as a power of x?
x^(ln(2)/ln(x)-1)
What is the integral of 1 divided by xln2x?
0.5
Does 1 over n converge?
No. ∑(1/n) diverges. It is the special infinite series known as the "harmonic series."
What is the antiderivative of e to the power of one divided by x?
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
What is the infinite limit of 1 divided by ln x?
The limit should be 0.
What is the integral of 1 divided by x-2?
3
How the value pi(3.14) is calculated?
Pi is the ratio of the circumference of a circle, to its diameter. In ancient times, it was approximated by inscribed and circumscribed polygons - the more sides the polygon had, the more accurate the approximation would be. Nowadays, infinite series are know that let you calculate pi. One well-known series of this type is:pi / 4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11... This series doesn't converge quickly; that means that you need to calculate lots of terms to get a certain degree of precision. Fortunately, other series are known that converge more quickly.
What is the derivative of y equals xlnx?
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
What is the integral of 1 divided by x with respect to x?
∫ (1/x) dx = ln(x) + C C is the constant of integration.
What does ln 1 equal?
ln 1 = 0 e0=1
Simplify In e to the 7th power?
It depends. If you mean (ln e)7, then the answer is 1, since (ln e) = 1. If you mean ln(e7), then the answer is 7, since ln(e7) = 7 (ln e) and (ln e) = 1.
What is the anti derivative of x divided by x squared minus 1?
The antiderivative of x/(x2-1) is ln(x2-1)/2. Proof: (ln(x2-1)/2)' = (1/(x2-1))*(x2-1)'/2=1/(x2-1)*(2x/2)=x/(x2-1).
