integration questions from essential math methods

[lanvins]

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

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

3. upper limit 36, lower limit 0  dx/(2x+9)= loge(k), then k is:

Thanks

[Collin Li]

Using the quotient rule:

[lanvins]

thanks,

[xox.happy1.xox]

2. y= loge(x), with point (e,1)

Find derivative,

dy/dx = 1/x

let x=e

dy/dx = 1/e = m

Use the formula y - y1 = m (x - x1), substitute y1 = 1, x1 = e, m = 1/e

y - 1 = 1/e (x - e)

y - 1 = x/e - 1

y = x/e

(Need to learn to use Latex, first try at helping somebody at maths... I wouldn't be surprised if it was wrong )

[lanvins]

nah it's right, thanks

[dcc]

3.

[lanvins]

where did the 2 come from?

[dcc]

where did the 2 come from?

I put the 2 there so that the integral could be expressed in the form .  Notice the term out the front of the integral, so the 2 and the 0.5 cancel each other out, leaving the answer the same.

[lanvins]

oic thanks,