2007年12月6日 · ln x^2 = 2lnx (lnx)^2 = (ln x)*(lnx) so no they are not equal (there may be a value for which they are but ...

2009年1月15日 · Find the intervals on which f(x) = ln(x² + 1) is concave up I got critical points to be -1, and 1 I checked by the first derivative that from - infinity to 0 the slope is negative and from 0 to positive infinity the slope is positive, i get confused about writing the intervals.

2010年1月16日 · u= ln(x2+y2) is a harmonic function find a harmonic conjugate function v and the analytic function f(z) ? S.

2010年6月9日 · Hey, perhaps the numerator \ln{x}^2 instead of \ln^2(x), which is little easier and probably more common? In any case, it can't get clearer than Tom's posts, so try to follow them. I don't think there is a way

2011年2月28日 · |f(x1) - f(x2)| = |cos(ln(x1) - cos(ln(x2)| = |- 1/2 sin (lnx1 + lnx2)/2 sin (lnx1 - lnx2)/2 | = = 1/2 |sin(ln(x1x2)/2) sin (ln(x1/x2)/2)| <= 1/2, so the assumption of uniformly continuity is performed at this interval. Is my solution right ? 4)f(x)=x2 tan-1x [0, infinity) My solution : I think it is the same on the first question

2011年2月28日 · Another one I'm currently stuck on: "Let f(x,y)=x^2+ln(y). Find the average rate of change of f as you go from (3,1) to (1,2). Find the instantaneous rate of change of f as you leave the point (3,1) heading toward (1,2)." What exactly …

2010年6月27日 · I seem to have totally messed up this problem because my results do not make sense. Could anyone please show me where I went wrong? Many thanks. The weekly demand for propane gas (in 1000s of gallons) from a particular facility is an rv X with pdf f(x)=2(1-\\frac{1}{x^{2}}) for 1\\leq x\\leq2...

2013年2月9日 · The area A of the region S that lies under the graph of the continuous function is the limit of the sum of the areas of approximating rectangles: (a) Use this definition to find an expression for the area under the curve y = x3 from 0 to 1 as a limit A= lim n- …

2021年5月24日 · 3. "Find an expression for the sum of the first 35 terms of the series ln x^2 + ln x^2/y + ln x^2/y^2 + ln x^2/y^3 + ln x^2/y^4. Giving your answer in the form ln x^m/y^n, where m, n are natural numbers." For this one, I got ln x^2a - ln y^s, a being the number of terms, s being the sum of the numbers between 1-34 (595). Thus, I get 2a ln x - s ...

2018年4月30日 · Question: Consider the function \\frac{2x}{1+x^2}. What is the radius of convergence for the Maclaurin Series approximating this function? My thoughts: I can take the derivative a bunch of times to recognize a pattern. I find that the series essentially becomes an alternating geometric...