Posted by **Anonymous** on Sunday, April 22, 2007 at 4:20pm.

consider the curve in xy-plane by x=e^t and y=te^(-t) for t is greater or equal to o. the slope of the line tangent to the curve at the point where x=3.

all the answer choices are decimal points. a is 20.086, b is .342, c is -.005, d is -.011 and e is -.033

so what i did is that since these are parametric equations i used the formula dy/dx=(dy/dt)/(dx/dt) to get the derivative to get the slope. but when i use the y-y=m(x-X) equation to get line, how do i get y.

you are on the right track, I would have done the same thing.

lets check our derivatives.

I had

dx/dt = e^t and dy/dt = (e^-t)(1-t) after using the product rule for that one and then simplifying.

so my(dy/dt)/(dx/dt) = (1-t)/(e^2t)

I need the t value when x=3

3=e^t, so t=ln3

then dy/dx = (1-ln3)/e^(2ln3)

= -.0109.. which was one of the choices.

BTW, did you realize that e^(2ln3) = 9 ?

## Answer This Question

## Related Questions

- calculus - 1. Given the curve a. Find an expression for the slope of the curve ...
- 12th Grade Calculus - 1. a.) Find an equation for the line perpendicular to the ...
- Calc AB - Suppose that f(x) is an invertible function (that is, has an inverse ...
- calculus - Consider the curve defined by 2y^3+6X^2(y)- 12x^2 +6y=1 . a. Show ...
- last calc question, i promise! - given the curve x + xy + 2y^2 = 6... a. find an...
- Calculus - Consider the curve given by y^2 = 2+xy (a) show that dy/dx= y/(2y-x...
- calculus - Consider line segments which are tangent to a point on the right half...
- Calculus - Show that the curve y=6x^3+5x-3 has no tangent line with slope 4. The...
- Calculus - The slope of the tangent line to a curve at any point (x, y) on the ...
- calculus - Find the slope of the tangent line to the curve (sqrt(4x+y))+(sqrt(...

More Related Questions