Recent content by sinbad30

I am given Z = f (x, y), where x= r cosθ and y=r sinθ I found ∂z/∂r = ∂z/∂x ∂x/∂r + ∂z/∂y ∂y/∂r = (cos θ) ∂z/∂x + (sin θ) ∂z/∂y and ∂z/∂θ = ∂z/∂x ∂x/∂θ + ∂z/∂y ∂y/∂θ= (-r sin θ) ∂z/∂x + (r cos θ) ∂z/∂y I need to show that ∂z/∂x = cos θ ∂z/∂r - 1/r * sin θ ∂z/∂θ and ∂z/∂y = sin...

Given the first order ODE y' = 2 * y^3 * x, plot the isoclines corresponding to slopes m = +1 and m = -1. My answer: The isoclines are given by m= 2 * y^3 * x or y=(m/(2*x))^1/3 The slope elements on the isocline y=+- (m/(2*x))^1/3 all have gradient m For m = 1, the isocline is y =...

Homework Statement Applying the definition of a limit to show that lim ((x^3 * y(y-1) ) / (x^2 + (y-1)^2) = 0 as (x,y) approaches (0,1) The Attempt at a Solution |x| = sqrt(x^2) <= sqrt((x^2 + (y-1)^2)) |y-1|=sqrt((y-1)^2)<= sqrt((x^2 + (y-1)^2)) |y|<= |y-1| + 1 via the...