Answered

Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Connect with a community of experts ready to help you find accurate solutions to your questions quickly and efficiently. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

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)?


Sagot :

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

We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.