Recent content by 4570562

Okay I think I figured it out. Suppose toward a contradiction that U=f=-mgy. Going back to the ball example that would mean U_{a}=-mgh K_{a}=0 U_{b}=-mg(-4.5+h)=4.5mg2-mgh K_{b}=4.5mg2 But that would violate conservation of energy since U_{a}+K_{a}≠U_{b}+K_{b}. However...

Let's take an example. Suppose you drop from rest a ball of mass m and let it fall for 3 seconds. You want to find the amount of work that gravity does on the object. There are three ways you could proceed. 1) Use W=\int\vec{F}\cdotd\vec{r} the line integral method. (Note that this...

Homework Statement My calculus book gives the following definition of a conservative vector field: A vector field F is called conservative if there exists a differentiable function f such that F=\nablaf. The function f is called the potential function for F. It then gives the...

Thank you very much. I knew it was something easy like that. I didn't see it because I kept going back to the limit definition of the derivative where it doesn't matter if you are interpreting the slope formula from the positive or negative direction. It seems that direction doesn't...

Homework Statement The evaluated partial derivative of f(x,y) with respect to x is -16 and 6 with respect to y at some point (x0,y0). What is the vector specifying the direction of maximum increase of f? Homework Equations The direction of maximum increase of f is given by...

Maybe you can take the gradient of a function of a single variable but just not the directional derivative? It seems to me now that the directional derivative wouldn't make any sense for f(x) because you can't vary x in a "direction". Varying x in the negative or positive direction still gives...

Seems right to me.

Homework Statement Is it possible to take the directional derivative of a function of a single variable? For example if f(x)=sinx and the unit vector specifying the direction is u=<cos pi/4, sin pi/4>, then could you say that duf = .5*(sqrt2)*cosx ?

Not quite sure, but maybe you do ∫f(y) dy from 0 to 10/45?

Thank you so much. cos theta = .5 implies that theta is pi/3 , which would make it work both ways. I can't tell you how long I have been just staring at this problem. Thanks.

Homework Statement Find the magnitude of the vector product w ⃗x u, where w=<1,0,1> and u=<1,1,0>. Homework Equations ||w x u|| = ||w|| ||u|| sin θ cos θ = \frac{w.u}{||w|| ||u||} The Attempt at a Solution w ⃗x u ⃗= -i ̂+j ̂+k ̂ ‖||w ⃗x u|| ⃗ ‖= √3 but...