2018年10月1日 · The question demands an answer to when ln(x+y) can be considered to equal ln(x)+ ln(y) and we are asked to use contour to prove this but the concept of contour does not entirely make sense to me. A...

Let ln x = ∫x11 t dt. How do I show that ln (xy) = ln x +ln y where x and y are positive reals. I read the following proof from Limaye book. Fix y ∈ (0, ∞). Consider f(x) = ln xy -ln x. Then f ′ (x) = 1 xy. y − 1 x = 0 ∀ x ∈ (0, ∞). ∴ f is constant. f(x) = f(1) = ln y - ln 1 = ln y. ∴ f(x) = ln (xy) − ln x = ln y ln (xy) = ln x + ln y I feels that this proof is so ...

2017年10月4日 · I was solving for the differential equation xy ′ = y(lnx − lny), y(1) = 4 and x> 0 My work The equation, I think, can't be categorized into variable-seprable, exact, homogenous, or others, unless modified. Modifying the differential equation above: xy ′ = y(lnx − lny)

If y = ln x y = ln x, then x = Ay x = A y, how do I prove that A = e A = e? There's another method by which I tried to arrive at the inverse of natural logarithm of x x.

2019年2月1日 · Hint: Take the natural logarithm on both sides of the equation which gives you ln(y) = ln(x)ln(ln(x)). Now all you have to do is to implicitly differentiate and use the product rule and the chain rule.

2011年11月7日 · If X is an exponential random variable with parameter λ = 1 , find the probability density function of the random variable Y=lnX. HINT: Find the cummulative distribution function. I don't understand what the hint saying, find the cdf of what? when λ =1, we have f (x) = e − x , Y=lnX implies X = e y , if I sub e y to f (x), it will be very hard to …

2016年7月6日 · setting the curvature equal to 0 gives a maximum of 0...is this correct? Determine the point on the plane curve f (x) = ln x where the curvature is maximum. You may need to review max-min methods from Calculus I to do this problem. Be sure to check that the curvature is max at the critical point.

I have the problem: Assuming y = ln(x) y = l n (x), and y = 0 y = 0, find the volume bound by these two lines and the point x = 2 x = 2 if the area were rotated around the x x -axis. I ended up with 2π∫2 1 ln(x)dx 2 π ∫ 1 2 ln (x) d x I would like to know if this is the correct way to set this problem up given the bounds.

2015年6月28日 · This is the line I have trouble with. I can see that it is true by putting numbers in, but I can't prove it. I know that e1 x =limh→0(1 + h)h x e 1 x = lim h → 0 (1 + h) h x, but I can't work out how to get from the above line to that.

2019年2月1日 · It's always helpful to visualize problems in calculus: Now, lets say we want the total volume of the region bounded by log(x) l o g (x), x = 4 x = 4 and y = 0 y = 0 rotated around the axis x = 5 x = 5.