The domain of f(x,y) = In xy is points (x, y) in the first quadrant Select one: O True O False

Q: 2. Show that the function u = p(xy) + Vry v(y/x) provides the equation = 0. dy? | dx²

A:

Q: Use the linear approximation to f (x, y) = √x/y at (9, 4) to estimate √9.1/3.9.

A: f(x,y)=xy at (9,4) to estimate 9.13.9

Q: Show that the function u e(xy) + Vry V(y/x) provides the quation = 0. dy?

A: Again differentiate,

Q: Consider f(z, y) = Vzy+ 2y? ry- %3D Approximate f(2.4, 1.04) by using the tangent plane.

A: f(x,y)=xy+2y2

Q: Let f (x, y) = xy2 + 5. Evaluate df/dy at (x, y) = (2, -1) and interpret your result.

A: Given: f (x, y) = xy2 + 5.

Q: The domain of f(x,y) = ln xy is points (x, y) in the first quadrant. Select one: O True O False

A: Domain  set of all input values where function defined

Q: Express in form y=f(x) by eleminating the parameter x = t + 3, y = 4t

A:

Q: Let f(x, y) = . Use the Linear Approximation at an appropriate point (a, b) to estimate…

A: Given,f(x,y) = x2y2+1To estimate,f(4.02,0.93) using the LinearApproximation at an appropriate point…

Q: Find fryz from the functions f(x, y, z) = 4x³y² – e²y* ++ 4y – x16 %3D - |

A: To find the third order partial derivative of the function fxyz f(x,y,z)=4x3y2-ezy4+z3x2+4y-x16

Q: the linear approximation for f(x,y) = sqrt (y+cos^2 x) at (0,35) is ?

A:

Q: Calculate fxxyz for f (x, y, z) = y sin(x + z).

A: We first differentiate the given function with respect to x twice. Then y and z will be treated as…

Q: Use the Linear Approximation to f(x, y) = x/y at (9, 4) to estimate 9.1/3.9.

A:

Q: Calculate fxxyz for f(x, y, z) = y sin(x + z).

A: For a function in several variables, partial derivative with respect to one variable say x can be…

Q: Consider f(x, y) = x³y+ 2xy? Approximate f(2.1, 1.03) by using the tangent plane.

A: Given f(x, y) = x³y + 2xy² Find f(2.1, 1.03) using tangent plane.

Q: Find fr, fy, and fz. f(r, y, 2) — вуzIn(4ry) fz fy f: =

A:

Q: Find fz(x,y) and fy(x, y) given f(r, y) = csc yArcsin(r²).

A:

Q: Given f(x, y) = et" Y° – a°y°, show that fæy = fyx· 93 fyæ- %3D

A:

Q: Find f, and fy. f(x, y) = 5x In xy %3D %3D fy =

A: Solution: The objective is to find the partial derivatives

Q: Find f(x) if y = f(x) satisfies %3D dy 42ya3 %3D dæ and the y-intercept of the curve y = f(x) is 4.…

A: Given that, y = f(x) and   dydx=42yx13 and y-intercept of the curve y = f(x) is 4. we have to find…

Q: What is fx , where f (x, y, z) = (sin yz)ez3−z−1√y ?

A: Given, f (x, y, z) = (sin yz)ez3−z−1y

Q: Find the linear approximation of the function below at the indicated point. f(x, y) = V 17 – x2 –…

A: Givenf(x,y)=17-x2-4y2  Point (2,1)

Q: Find f, and fy. 'y' f(x, y) = 2x In xy

A:

Q: 2. Show that the function u = p(xy) + Vry ý(y/x) provides the equation n, = 0. dy? U -

A:

Q: Find a linear approximation to the function f(x,y) at the indicated point. 2x°y f(x,y) = at (5,1) 1…

A: Linear approximation to the function f(x ,y) at (a, b) :       L(x ,y) = f(a ,b) +(x-a) f x (a, b) +…

Q: Let F(x, y) = G , y 1 )- Calculate the work against F required to move an object from (1, 1) to (3,…

A:

Q: Find the linear approximation to f(x)= cot (x) LCx) = f (a) + f'Ca) (x-a). near a=" as

A:

Q: Consider the finction f(x,y) = x² + xy – 5x – y+ 1. Then:

A:

Q: |dx + N(x,y)dy = 0 x² + y,

A:

Q: Find the local linear approximation to f(x, y) = 4x² + y² at P(2,3)

A: We have to find the linear approximation of above function at (2,3) please see the explanation…

Q: H.W: Find fr, fyand f if f(x,y, z) = x-Vy +z

A:

Q: Fínd a differentiable curve y(x) that minimizes J = +

A: The objective is to find the differentiable curve yx that minimizes J=∫01y'x2+c2yx2dx if y0=0 and…

Q: Given that f(x, y)= 2x* +3x'y+6xy'-y. Find: i. f ii. f, iii. fx XX iv. fy v. Show that xy = f

A:

Q: - x'yt, show that fxy = fyx. 7,4 Given f(x, y) = et*

A: Given f(x,y) = e(x^4y^9) - x7y4

Q: Q4: Find f for f(x,y,z) = xcos(y + 3z) + xyz at the point ( 1,3,-1)

A:

Q: Find fr, fy, and fz. f(x, Y, z) = 4yz In(6ry) fz = fy = f: =

A: Given: f(x, y, z)=4yz ln(6xy)

Q: (a) Let f(r, y) = x - 3ry + 18y, where 3r?y- y- 6x = 0. Prove that f(r, y) has extrema at the points…

A: Calculate partial derivative of f(x,y) with respect to x and y ,

Q: Given f(æ, y) = e"" Y' – z°y", show that fæy = fyæ.

A:

Q: Use the Linear Approximation off (x, y) = ex2+Y at (0, 0) to estimate f (0.01, -0.02). Compare with…

A: By the method of linear approximation, if we are given a differentiable function f in two variables,…

Q: Show that the function u = p(xy) + VrY v(y/x) provides the uation x2 = 0. dy?

A: First find the partial derivative of the given function with  respect to x :

Q: Find the domain of f(x, y) = Vy+I y(1-x²)

A: Given: f(x,y)=y+1y1−x2 The domain of functions of two variables, f(x,y) are regions from two…

Q: Suppose that f(x, y) = e 42? - ly + 7z + 2y then find the discriminant of f.

A:

Q: Show that the function u = p(xy) + Vry v(y/x) provides the quation = 0. dy?

A:

Q: Use the linear approximation of f(æ, y) = e+y at (0, 0) to estimate f(-0.03, -0.03)

A:

Q: Let y = f(x1, x2, w), where x1 = 2w2 and x2 = w+1. Find dy/dw.

A:

Q: If f(z) = sin(z 2) = U(x, y) + iV (x, y), determine U and V . Verify that the C-R conditions are met…

A:

Q: Find f, for f(x, y) = | cos(r*) dt.

A:

Q: f(x, y) = /32² + 3y fz(4, 5) = VT23 %3D

A:

Q: X+Z+3Siny X +2y-2

A:

Q: Find the extrema of the function f (r, y) = y(x² + (In y)²), y > 0.

A: Second derivative test of two variable  function is Da,b=fxxa,b×fyya,b-fxya,b Then  If Da,b<0,…

Q: Find all values of x and y such that fx = 0 and fy = 0 simultaneously. 13. f(x,y) = e*»+y?

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.