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(1 point) Let f(x, y) = (- (3х +y)*. Then д?f дхду д'f дхдудх = д'f...
(1 point) Consider the function defined by ?(?,?)=??(9?2+5?2)?2+?2F(x,y)=xy(9x2+5y2)x2+y2 except at (?,?)=(0,0)(x,y)=(0,0) where ?(0,0)=0F(0,0)=0. Then we have ∂∂?∂?∂?(0,0)=∂∂y∂F∂x(0,0)= ∂∂?∂?∂?(0,0)=∂∂x∂F∂y(0,0)= Note that the answers are different. The existence and continuity of all second partials in a region around a point guarantees the equality of the two mixed second derivatives at the point. In the above case, continuity fails at (0,0)(0,0). (1 point) Consider the function defined by F(x, y) = xy(9x2 + 5y2) x2 + y2 except at (x, y) = (0,0)...
i need help with all parts. i will rate. thank you very much. Suppose u=f x+y ху is a differentiable function. Which equation must be true? ди ди дхду = 0 од? д?u дх2 ду? + = 0 х2. ди ди - у. дх ду = 0 ди y- дх ди Х- ду = 0 O None of the above Suppose the position vector is given by F(t) = = <t, t², 2) Then at time t = 1, the...
Find the first partial derivatives of the function z = (3х + 8y)1. дz 1. ІІ дх дz. 2 . ІІ ду
Let F = (x,y) and C be the triangle with vertices (0,5) and (3,0) oriented counterclockwise. Evaluate 9. Fodr by parameterizing C. Use a parametric description of C and set up the integral. 1 $ F•dr=So dt 0 Choose the correct answer below and, if necessary, fill in the answer box to complete your choice. of O A. For F = (f,g), evaluating the integral using дх дg and ду = results in a nonzero value of og OB. For...
I need help with Number #3 3) (2 marks) Write down analogous expression to equations (5)-(8), assuming a Galilean transformation: x' = X – ut, y' = y, z' = z and t = t. и д с2 Әt' (5) (6) д дх д ду д дz д at д дх? д ду" д дz! д Y Әt! (7) Ә и- Әr? (8) Hint: you need to use the chain rule. 3) (2 marks) Write down analogous expression to equations...
Derive the inverse Lorentz transformation for the partial deriva- tives, (5 и д с2 Әt! (5) (6) а дх а ду а дz а Әt д 7 Әr? ә ay' а дz! а 7 де? (7) ә - (8) Әr! Hint: you need to use the chain rule. Write down analogous expression to equations (5)-(8), assuming a Galilean transformation: x = x – ut, y' = y, z' = z and t = t.
1. Solve equation Ә2u(x, y) - 0 — дхду with following boundary conditions: и(0, y) = y + 1, и(x,0) = х2 + 1. 2. Find solution of the equation: д? u(x, y) - u(x, y). дхду
Step 2 For F(x, y, 2) = 8exy sin(2) ј+ Зy tan- n (3) k, we have the following. дR - дQ ду дz E др — aR дх дz X X X дQ дх ӘР ду Submit Skip (you cannot come back)
ид С2 at (5) а ду ә (6) д 7 Әr! д ay' а д! а Y де (7) дz а at — и а д" (8) Hint: you need to use the chain rule. 3) (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 point) Let F = xi+ (x + y) 3+ (x – y+z) k. Let the line l be x = 4t – 3, y = — (5 + 4t), z = 2 + 4t. = (20, Yo, zo) where F is parallel to l. (a) Find a point P P= Find a point Q = (x1, Yı, z1) at which F and I are perpendicular. Q - Give an equation for the set of all points at which F...