(x, y) = (b) 1 1 (d) 1/2 Does not exist. (x, y) = Ty³ x² + y6 = Find limf(x,y) along the path x = y³. (x,y) → (0,0) xy³ x²+y6° (x,y)→(0,0) Find f(x,y).

Q: Calculate r' (t) and T(t), where r(t) = (2t - 7,2 – 5t, 3 + 5t). r' (t) = (2 T(t) = -5 5

A:

Q: Given f(z, y) = – 3z' + ry° + 5y², find fr(x, y) = | fy(z, y) = |

A:

Q: Consider the function f defined by 1²+y² V12+y?+1-1 ,2 f(r, y) = %3D lim(7.y)¬(0,0) f(x, y) =

A:

Q: The temperature at a point (x, y) is T(x, y), measured in degrees Celsius. A bug crawls so that its…

A:

Q: (x* + y° ) In (x² + y* ). (x,y)= (0,0) f(x, y) = k +1, (x, y) = (0,0)

A: If f is continuous then lim (x, y) tends to (0, 0) =k+1 And using l hospital rule.

Q: For the function f(x,y) = 100 - x^2 - y^2 a) Draw the cross-section of f(x,y) with x fixed at x =…

A: "Since you have posted a question with multisubparts, we will solve the first three subparts for…

Q: An object is traveling along the line y = 2x + 1 heading up and to the right. If the temperature at…

A:

Q: f(x, y) = √√2x² + 5y² fz(0, 1) =

A:

Q: 교꾸가고 (a, y) + (0,0) (x, y) = (0,0) f(x, y) = x2+y2 is discontinuous at (0,0).

A:

Q: Find the limit of the function f(x, y) = 3e"-10y (x, y) → (0,0). as lim (x,y)→(0,0) 3e*-10y %3D

A: We will solve limit using simple method

Q: fo Find mini

A: Given :   fx, y=x+y+27xy

Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = sec-1 (x + yz)

A: Given that f(x, y, z)=sec-1(x+yz)

Q: Let f(x, y) = xy+ + 2x²y + 4y5 (a) Find fr- (b) Find fy-

A:

Q: f(x, y, z) = z°y?lna fazyzz =? IIY -2z2 O A. 12y2z2 В. 2x2 -12yz O C. x2 y24 O D. x4

A: Partial derivatives

Q: f(x, y) = xsin²y + y² cosx, Find fxy a. sin² y - y² cosx b. 2xsinycosy-2ysinxcosy c. 2sinycosy -…

A: We need to find fxy.

Q: Consider f(x, y) = xy(²-x²) x² + y² 0 if (x, y) = (0,0) if (x, y) = (0,0) . Show that fay(0,0) = 1…

A:

Q: Let f(1,y) = (r+ay°,r²y°,2r + by), g(u, v,w) = (3u² + bv² + w°, uvw). Find the derivative of…

A: Let f(x, y)=x3+ay2, x2y3, 2x+by,  gu, v, w=3u2+bv2+w3, uvw. We need to find the derivative of fgu,…

Q: The graph of y=x'-3x-24x +32 is concave upward on the interval (1, oo) because: O'=y"=0 Oy' is…

A: The given function is y=x3-3x2-24x+32

Q: Consider the function. f(x, y) = 2(y + 1)x² Identify the point(s) on the graph of f at which the…

A:

Q: Find fr and fy for f(x,y) = I+y fz = /(r+y)? and fy = /(r+y)2

A:

Q: domain and range of f(x,y)

A: Given: f(x,y)=9-x2+y2 -42 To find: Domain and range.

Q: 3z2+x 30. If z – xz – y = 0, prove that- =- ax dy (3z²–x)³*

A: Let's find.

Q: Let s(xy) = x²+y²_2x – 16y +10 =0 a cirdle be L (xy) = X-5y + 10=0 be a line.

A: