Let f(x, y) = /175 — 42? — Зу? - then evaluate f(2, 1).

Q: 1- f(x,y) = In(x² + y?) at (1,1)

A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as…

Q: 4xy* :- find f,,f, at point (4,1) for f(x,y) = x’e**Y

A: I have used partial differentiation

Q: Sx, ifx 1 f(x) = Show that f is R- integrable.

A: R- integrable function

Q: f(x,y)=x² +16xy + y² +8

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Q: Prove that = va² – x* if y =(f)sin~+ () + (9)v&* - x²

A: Differentiation wrt x

Q: 2. Find a function f(r, y, 2) which makes (yz?, rz?, f(r, y, z)) conservative. Show that your answer…

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Q: Suppose f(x,y)=xex. At the point (2,0), in what direction is the directional derivative maximized? |

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Q: Find the partial derivative f(x,y) = x7y fx(x,y) = ? fy(x,y) = ?

A: The given function is: f(x,y)=x7y

Q: Use the second-derivative test to show that the function f(x, y) = x²eY – y²e* has a saddle point at…

A: A point (a,b) of function f(x,y) is said to be the saddle point if it is a critical point…

Q: Determine (x, y) and 2(x, y), where f(x, y) = X sen(xy) %3D y

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Q: Let { sin(r-y) |r|+ |y| 0 (x, y) = (0,0) f(x, y) = Is f continues at the origin? Why?

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Q: Suppose that f(x, y) : at which {(x, y) | 0 < x < 4, – x < ys va}. 1+ x D

A: Consider a given function:  The objective is to evaluate the following double integral of fx, y…

Q: Suppose F(x,y)=sin²(xy +e"), where x=u² +v and y = In(u² +v). Find the . ƏF ¸ ÔF value of when u =1…

A: The given function is: F(x,y)=sin2xy+eywhere:x=u2+v         and         y=lnu2+v

Q: · F(x) = 5* (S₁²¹6 (√₁+ u²) du) dt

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Q: Let f (x,y) =In Then f „(1, – 1) =... 3x²+ 4y3

A: This is a problem of partial.

Q: dx Show that f - In|ax + b| + C where a # 0. ax+b

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Q: Which direction is the directional derivative of the function f (x,y, z) = x2 – 2yz at point…

A: Solution: The function is fx,y,z=x2-2yz The point is P1,1,1 We have to find the direction in which…

Q: Suppose f(x,y)=xex. At the point (2,0), in what direction is the directional derivative maximized?

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

A: f(x,y)=(x3+ay2,x2y3,2x+by)g(u,v,w)=(3u2+bv2+w3,uvw)To Find: Derivative of f(g(u,v,w)) using the…

Q: Compute fe F d where F (x, y) = x² + y). (2xy + x, Hint: Is F conservative?

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Q: Find fr, fy and fz. f(x, y, z) = x – Vy² + z? |

A: Given f(x,y,z)=x-y2+z2. The objective is to find fx,fy and fz.

Q: . Suppose that F(t) is a twice-differentiable function of one variable. Define the function f(x, y)…

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Q: Show that the function defined by xy √x²+y² f(x, y) {{ = 0 if (x, y) = (0,0) is not differentiable…

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Q: of Let f(x,y) = xy° +7. Evaluate at (x,y) = (-7,1) and interpret the results. ду -

A: In this question we have find δfδy at (x, y)=(-7, 1)

Q: Find fg, fyand f; if f(x,y,z) = x - Vy² + z²

A: Given:     To determine: Partial  derivative  fx, fy, fz

Q: 2 Find f, fyand f. if f(x, y, z) = x-Vy + z°

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Q: Determine k so that f(x, y) = kx(x- y) for 0<x <1,-x< y<x is a joint pdf.

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Q: Q2 (A) At what points f(x, y, z) in which the function f(x, y, z) = continuous? is

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Q: Find f, and f, for f(x,y)=y In (3x +4y). fx fy

A: When the partial differentiation is done with respect to a specific variable, then all other…

Q: Find the best linear approximation, g, to f on the interval [0, 1]. (x) = 2/x g(x) %3D

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Q: Let f(r) = Vt3 +1 dt for r2 3. 3

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Q: Let f (x, y) = 2x³ + 4y³ + 19xy Find D = frx · fyy - fey at the point (2,2)

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Q: Find the linear approximation of the function f(x) = Vr + 15 at a = 1 and use it approximate the…

A: Given, f(x)= (x+15)1/4 a=1

Q: Find He valve of fe2) when fg functions such that are dilferentrable %3D g(x) >o 1 for all x, while…

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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: What is the gradient of f(x, y, z) = x³z2 + y³z +125z - 1 at P(5,5,-1) ?

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Q: The gradient of f(x, y) = xy at (x, y) = (3, 1) is

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Q: Calculate F- dS where F (3ry², re", z*)

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Q: Use the limit to find partial derivative of…

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Q: Let f(r,y, z) = x² + 3x°y + z°, g(u, v) = (u² + v², uv, 3u – 2v). Find the derivative of f(g(u, v))…

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Q: Integrate from f(x) = x4 from 0 to 1 by (Trapezoidal Rule) with h = 1, h = 0.5, h = 0.25 and…

A: Here, f(x)=x⁴ So, I=  Integrate from f(x) = x⁴ from 0 to 1. Now we can solve by Trapezoidal rule,…

Q: 4. Let F : R² → R² defined by F(x,y) = (2x +3y, –x +y). Is F a linear? Why?

A: Given

Q: Consider function f(x, y) = x cos(TxYy) + x³y. .3,

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Q: Calculate fz(2, 3, 1), where f(x, y, z) = xyz.

A: Given,          fx,y,z=xyz

Q: Integrate f(x) = 10 ( 1 – x)9 where 1 ≤ x ≤ 3, Using Boole’s rule

A: The function f(x)=101-x9 where 1≤x≤3. We have to integrate this integral using the Boole's Rule.

Q: What is the maximum value of the directional derivative of f(x, t) = f (x, t) = x² + t²/8 – 10 at…

A: Note: The directional derivative of a function is the rate at which the function changes at a…