In Exercises 71-74, find a function z = f(x,y) whose partial deriva- tives are as given, or expla...
(4 marks) Derive the inverse Lorentz transformation for the partial deriva- tives, u a cat (5) (6) a ar a ду a дz a at a ar' a ay a az! a 7 at' (7) u (8) ar' Hint: you need to use the chain rule. (2 marks) Write down analogous expression to equations (5)-(8), assuming a Galilean transformation: x' = x -ut, y = y, z = z and t' = t.
1. What are the four basic shapes/combinations of first and second deriva tives? One common problem is forgetting to check where the first or second deriva tive does not exist. These are also critical/inflection points. Consider the x = t-sin(t y 1-cos(t) parametric function where-2π < t < 2T. 2. What are the first and second derivatives? 3. Where are the first and second derivatives equal to 0? 4. Where are the first and second derivatives undefined? 5. Where is...
1. Given f(x,y) = z as z = 2 +y find: (a) the partial derivative f(x,y). (b) the partial derivative fy(2,y).
Find the constrained extrema of the function f (x, y, z) = x + y + z on the plane given by the equation x^2 + 2xy + 2y^2 + 3z^2 = 1.
9. Find the local extrema and increasing and decreasing intervals for the function whose deriva- tive is given below. (Note: This is the first derivative that is given. You do not need to find the derivative!) f'(x) = ? (7 - 50) √9 – 2²
2. Consider the following function: Compute each of the following: Hint: There is probably a better way to compute these than to just mindlessly compute all ot partial derivatives in the order given 3. Is there a function f(x, y) with partial derivatives f, (z, y) = 2r + 5e" + 4y and f,(x, y) = 2y + 5e" + 2x? If so, give an example of a function with these partial derivatives. If not, say why not
2. Consider...
1. Find the first and second partial derivatives: A. z=f(x,y) = x2y3 - 4x2 + x2y-20 B. z=f(x,y) = x+ y - 4x2 + x2y-20 2. Find w w w x2 - 4x-z-5xw + 6xyz2 + wx - wz+4 = 0 Given the surface F(x,y) = 3x2 - y2 + z2 = 0 3. Find an equation of the plane tangent to the surface at the point (-1,2,1) a. Find the gradient VF(x,y) b. Find an equation of the plane...
DUE DATE: 23 MARCH 2020 1 1. Let f(x,y) = (x, y) + (0,0) 0. (x, y) = (0,0) evaluate lim(x,y)=(4,3) [5] 2r + 8y 2. Show that lim does not exist. [10] (*.w)-(2,-1) 2.ry + 2 3. Find the first and second partial derivatives of f(x,y) = tan-'(x + 2y). [16] 4. If z is implicitly defined as a function of x and y by I?+y2 + 2 = 1, show az Əz that +y=z [14] ar ду 5....
Find the exponential function f(x)=a^x whose graph is given.
Find the exponential function f(x) = ax whose graph is given. f(x) y 20 (2, 16) 15 10 5 -3 -2 - 1 2 3
96. Consider a vector field F(x, y, z) =< x + x cos(yz), 2y - eyz, z- xy > and scalar function f(x, y, z) = xy3e2z. Find the following, or explain why it is impossible: a) gradF (also denoted VF) b) divF (also denoted .F) c) curl(f) (also denoted xf) d) curl(gradf) (also denoted V x (0f) e) div(curlF) (also denoted 7. (V x F))