Integration (1 Viewer)

[lanvins]

1. Find the coordinates of P, the point of intersection of the curves y=e^x and y=2+3e^(-x). If these curves cut the y-axis at points A and B respectively, calculate the area bounded by AB and the arcs AP and BP. Give you answer correct 3 decimal places.

2. differentiate f(x)= loge(x) / (x^2+1)

3. Find the equation of the tangent of y= loge(x) at the point (e,1)

4. upper limit 36, lower limit dx/(2x+9)= loge(k), then k is:

Thanks

 

[conics2008]

sounds like home work.. cant be stuffed.

 

[Slidey]

1) cbf
2) ln(x)*(x^2+1)^-1, product rule:
derivative: 1/(x^3+x) - 2x*ln(x)/(x^2+1) = (1+2x^2*ln(x))/(x^3+x)
3) y'=1/x, y'(e)=1/e
tangent: y=x/e+b, 1=e/e+b so b=0
tangent: y=x/e
4) Pardon wtf bbq?
Int dx/(2x+9) from 36 to a = ln(k)
Int dx/(2x+9) = ln(2x+9)/2
For terminal 36, the answer is ln(81)=2ln(9), but you didn't specify a.

If I had to guess I'd say that a is some number such that 2a+9 is a square or a power of 4. Let's say that 2a+9=b^2, then ln(k) = ln(9/b) or ln(b/9).

Something like that.