c. Let f(x,y)=⎩⎨⎧​y2+2x22x2+3xy​+xy0​ if (x,y)=(0,0) if (x,y)=(0,0)​ i. Find fx​ and fy​ when (x,y)=(0,0) ii. Find fx​

[answerhappygod]

C Let F X Y Y2 2x22x2 3xy Xy0 If X Y 0 0 If X Y 0 0 I Find Fx And Fy When X Y 0 0 Ii Find Fx 1 (38.24 KiB) Viewed 35 times

c. Let f(x,y)=⎩⎨⎧​y2+2x22x2+3xy​+xy0​ if (x,y)=(0,0) if (x,y)=(0,0)​ i. Find fx​ and fy​ when (x,y)=(0,0) ii. Find fx​(0,0) and fy​(0,0) iii. Show that fyx​(0,0)=fxy​(0,0) 2. a. Find ∇f for f(x,y,z)=sin(xyz2)+xy at P=(1,−2,4) b. Suppose that the velocity of the point (x,y,z) in space is given by V(x,y,z)= 1+2x2++y2+3z270​ where V is measured in m/s and x,y,z in meters. i. In which direction does the velocity increase test of the point (1,−1,3) ? ii. What is the maximum rate of increase? c. Use the Mean Value Theorem to show that ∥lnp−lnq∥≤3∥p−q∥ for 1/8≤ z<w≤8 d. Determine the first(linear) and second(quadratic) order Taylor Polynomial approximations for f(x,y)=2xey+xy2 near the point (1,0). e. Show that following functions are functionally dependent by using Jacobian matrix. f(x,y)=x2+2y3g(x,y)=x−y​ 3. a. i. Find a symmetric matrix A such that Q(x)=xAxτ for each x∈R2.  Let Q(x)=x12​+5x1​x2​+x22​.  ii. Determine whether the above matrix is PD, PSD, ND or NSD (Definiteness).