Recent content by chemphys1

Homework Statement Show z(x,y) = cos(xy) is a solution of (∂z/∂x)y + (∂z/dy)x = (x+y) ( (∂2z/∂x∂y) + xyz) (question also attached if it makes it clearer) The Attempt at a Solution ∂z= (∂z/∂x)ydx + (∂z/dy)xdy ∂z/∂x = -ysin(xy) ∂z/∂y = -xsin(xy) what does it mean show it...

Thank you for the help, it really is appreciated!

is it as simple as follows: x = 0 y= 0 z = any positive integer?

I don't recognise this kind of question, how would I go about finding this vector?

f(x,y,z) = x2 + y2 + z2 which values of x,y,z does ∇f point in the positive z directionok so I know ∇f = i ∂/∂x + j ∂/∂y + k ∂/∂z which turns out to be ∇f = 2x i + 2y j + 2z k but how am I finding values so that z points in the positive direction? what does that even mean? ∇f is gradient...

Sorry, I really do not follow I find it hard to understand mathematical notation, so re: z = f(x/y) = x/y I can't see how to check the example

complete question is attached, but the information in the original post is correctly copied as far as I can see

Homework Statement If z(x,y) = f(x/y) show that x(∂z/∂x)y + y(∂z/∂y)x = 0 Homework Equations so I understand z(x,y) means I can write dz = (∂z/∂x)ydx + (∂z/∂y)x dyI do not understand the = f(x/y) bit though? does that mean this? df= (∂f/∂x)y dx+ (∂f/∂y)x dy and (∂f/∂x)y = -y/x2 (∂f/∂y)x =...

Homework Statement The activation energy and Arrhenius paramter can be found from its temperature dependence the Arrhenius equation k=Aexp(-Ea/RT) --> lnk=lnA - Ea/RT Given data is 5 temperatures with their corresponding k values Q1) From this data calculate A and Ea q2) Here A has...

Have I got this right, I integrate f(x) but with x = u-2 i.e integral of (u-2)^4 - 3(u-2)^3 etc with the new limits being 0.2 - 0? Not really sure what the point of the expansion I did was?

Thank you for the help! I've subsituted x = e^-z so dz = dx/-e^-z integral becomes 1/e^z(1+x)^1/2 (1-x^1/2) * dx/-e^-z e^z*-e^-z = 1 so 1/(1+x)^1/2 (1-x^1/2) dx = 1/(1-x^2)^1/2 and then e^-z = x e^-infinity = 1 hence new limits 1 to 0 I think that works?

Homework Statement sorry if question is unclear can't draw the integal sign out Show that Integral infinity-0 dz/((e^2z) - 1)^1/2 = integral 1- 0 dx/(1-x^2)^1/2 = pi/2 The Attempt at a Solution I can get from the second integral to pi/2, as the second integral is sin^1(1) =...

Homework Statement expand f(x) = x^4 - 3x^3 + 9x^2 +22x +6 in powers of (x-2) Hence evaluate integral, (limits 2.2 - 2) f(x) dx Homework Equations Taylor expansion for the first part integral f(x) dx with limits 2.2-2 The Attempt at a Solution Expansion of the function...

come up with this dD = E∂ε + εdE where dε = (∂ε/∂V)dV + (∂ε/∂T)dT overall dD = E [(∂ε/∂V)dV + (∂ε/∂T)dT] + εdE is that what I should be getting?