consider the curve y=ln(3x-1).let p be the point on the curve where x=2.

a) a write down the gradient of the curve at P.

b) The normal to the curve at P cuts the x axis at R.Find the coordinate of R.

(is the gradient of P 3/(3x-1)?

Question

20-09-2014
Mathematics

Answered

consider the curve y=ln(3x-1).let p be the point on the curve where x=2.

a) a write down the gradient of the curve at P.

b) The normal to the curve at P cuts the x axis at R.Find the coordinate of R.

(is the gradient of P 3/(3x-1)?

Answer :

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AndyBryer AndyBryer · Answer 1 · 2014-09-20T14:55:52-04:00

a. Yes you are correct that the gradient at any point is 3/(3x-1). However at point P it would be 3/(3*2-1)=2/5
b. The gradient of the normal would therefore be -5/2
We can use the general formula of an equation to get y-ln(5)=-5/2 (x-2)
Now multiply both sides by 2 to get:
2y-2ln(5)=-5x+10
Now when it crosses the x axis we know that y=0 therefore:
5x=10+2ln(5)
Therefore:
x=2+2/5 ln(5) when y=0
You could find an estimate of this number to be 2.64 (3sf) but this might not be sufficient

consider the curve y=ln(3x-1).let p be the point on the curve where x=2. a) a write down the gradient of the curve at P. b) The normal to the curve at P cuts the x axis at R.Find the coordinate of R. (is the gradient of P 3/(3x-1)?

Answer :

Other Questions

consider the curve y=ln(3x-1).let p be the point on the curve where x=2.

a) a write down the gradient of the curve at P.

b) The normal to the curve at P cuts the x axis at R.Find the coordinate of R.

(is the gradient of P 3/(3x-1)?