Posted by **John** on Sunday, October 18, 2009 at 3:24am.

An object is moving along the parabola y = 3x^2. (a) When it passes through the point (2,12), its horizontal velocity is dx/dt = 3. What is its vertical velocity at that instant? (b) If it travels in such a way that dx/dt = 3 for all t, then what happens to dy/dt as t --> +infinity? (c) If, however, it travels in such a way that dy/dt remains constant, then what happens to dy/dt as t --> +infinity?

- Calculus -
**Reiny**, Sunday, October 18, 2009 at 8:24am
dy/dt = 6x(dx/dt)

so at (2,12) dx/dt = 3

then dy/dt = 6(2)(3) = 36

If dx/dt is always 3, then dy/dt = 18x

so as x --> + infinity , 18x ---> + inf.

and dy/dt --> + inf.

for c) I think you meant to say,

"then what happens to dx/dt as t --> +infinity?"

if dy/dt = c

then c = 18(dx/dt)

dx/dt = c/(18x), now as x becomes larger and larger, what happens to the c/(18x) , and as a result, what happens to dx/dt ?

## Answer this Question

## Related Questions

- calculus - An object is moving along the parabola y = 3x^2. (a) When it passes ...
- Calculus - An object is moving along the parabola y = 3x^2. (a) When it passes ...
- math - An object is moving along the parabola y = 3x^2. (a) When it passes ...
- calculus - 2. An object is moving along the parabola y = 3x^2. a) When it passes...
- Calculus - 2. An object is moving along the parabola y = 3x^2. a) When it passes...
- physics - You throw a ball toward a wall with a speed of 25m/s and at an angleof...
- Calculus - A particle is moving around the unit circle radius = 1, at .6,.8 the ...
- Physics - An object is thrown from the top edge of a building at a speed of 21....
- Physics - Two objects are moving in the xy-plane. No external forces are acting ...
- Physics - Two objects are moving in the xy-plane. No external forces are acting ...

More Related Questions