Find f fy. - f(x.y.z) = x - Vy² + 22? + 2z² = (Type an exact answer using

Q: Find fy (x, y) for f(x,y) ry

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Q: ive of f(x, y, z) 1) in the dired

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Q: find f given f (z, y) = e + 2ry 4y at (0,3)

A: Topic- partial differential

Q: What is frz, fyy, and fyz of f(x, y) = In(y²")?

A: Given:           f(x,y)=lnyx2          fx=∂∂xlnyx2         Treating y as constant variable…

Q: of of and dy 6. For the function f(x.y) = sin ° (6x - 5y), find of df dy II

A: In partial derivative when take the derivative with respect to one variable consider other variables…

Q: Fundamental Theorem of Calculus.

A: ∫abfx dx

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

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Q: Given f (x,y) = x³ + y3 – 3y² – 3x² – 9y, find the critical points and use the Second Derivative…

A: solution :-

Q: af Find of f (4.v) = sin ) 1+ y

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Q: y = 0.25e2x – 4.5cosx ,using xl = 0 and xu = 1.5, at absolute relative error of 1% use false…

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Q: Find f, fy. f- f(x.y.z) = 3x - 4y 2. 2 +z?

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Q: of of For the function f(x,y)% 9x2- 3y°-4, find and dx dy of II

A: While calculating the partial differentiation of a function with respect to X we consider the other…

Q: 4. Use the contour integration to find f G dx. 1 x4+16

A: Answer: π/(16√2)

Q: he derivative of f(x,y)=10x^y at (e,1) in the direction of v = is

A: From the expression of the directional derivative:   D.D=∇fpx,y,z·a→a→   Given:…

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: ren f(x, y) = In Va²y3. What is = value of fy(1, 2)?

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Q: Find the relative extrema using both the first and second derivative tests. f(r) = 2x³ – 9x² + 12x.…

A: Consider: fx=2x3-9x2+12x. Critical point is the point where the derivative of the function is either…

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

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Q: Approximate X f(x) = e*over the interval [- 4, – 2] using 2 subintervals.

A: In this problem, Simpson 1/3rd rule is used to find the approximate value of e^x over the interval…

Q: Find the domain and range of the function f(x, y) = exy

A: Given information: The function fx,y=exy

Q: Use the second derivative test to find the local extrema of the function f(x, y) = x+ 2xy – 6x –…

A: Step 1: Find the partial derivativesfx and fy and put both equal to zero and we getcritical points…

Q: equation of line normal to f(x) = (x +4)1/2 at Q (0,3) is?

A: Given, f(x)=(x+4)12 To find: Equation of line normal to f(x) at Q(0,3)

Q: 5. Given that f (x, y) = sin y, determine fy(x, y).

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Q: A particle is moved along the x-axis by a force F(x) = x² + 5x – 6 . How much work is done in moving…

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Q: Find the linear approximation to the function f(x, y) = sin y --- |T at x, = (1, -2) 2 and use it to…

A: The solution is given as

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: ( 2x2 , xs1 Dose f(x) = continuous at x =1?why? %3D &+ 1 , x >1

A: Explanation of the solution is given below....

Q: Find the fourth derivative of f (z) = 2z¬3 Vā lal * sin (a) f(4) (z) =

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Q: given the function f(x) = (x+4)^2 + (y-2)^2 (i)find the critical points (ii)using the second…

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Q: Find the linear approximation of f(x) = (5 + x)n at x = 0. Use the approximation to estimate the…

A: fx=5+xn at x=0. Differentiating with respect to x, we get f'x=n5+xn-1 Now, f0=5+0n=5n &…

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

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

Q: Estimate the slope f'(3.5) for f (x) = sin(3x) using: a. Forward difference approximation with h =…

A: f(x)= sin3x x y y1 y2 y3 y4 3.3 -0.1557             -0.193       3.5 -0.3507   0.0139…

Q: Integrate the function f (z) = (z – 8i)² from z = 0 to z = 4 + 4i along the line x = y. 2

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Q: Find whether the function F-(* - y')i + (v² – 3x)j + (=* - xy)k is irrotational.

A: A vector field F is called irrotational if curl (F) = 0.

Q: The average rate of change of the function y = x² in the interval 2 sx< 5 is %3D

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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: Find fyxy. f (x, y) = x"y® – 20°y +x f yay YxY

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Q: 4. y2 +2xy 4, find y" Ans. y" = (x+y)

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Q: der to evaluate t son's 1/3rd rule e used at x = 0.C of the error of

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Q: Find fyy for f(x, y) = e* In(y).

A: The given function is fx,y=exlny.

Q: Find the linear approximation of f(x) = Vx-1 approximate 2.02. near a = 2. Use the result to

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Q: Obtain the MSE of f(x) = ex.

A: MSE = Maclaurin Series Expansion f(x)=ex formula f(x)=∑k=0∞f(k)(0)k!xk

Q: xyz f(x.y.z) = et ot function is given P(2,,4) in point fux + fyy + fzz colculate.

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Q: Use the Trapezoidal Rule with n = 4 to estimate f, x² dx. Compare the estimate with the exact value.

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Q: 4) f(x,y) =Vx +y Ans. f.= +y Vx + y?

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Q: 0If z-x"f), show that xZ+JZy=mZ.

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Q: find the degree of Precition @F(x)= X

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Q: Use the linear approximation to ƒ(x, y) 12x² at (3, 9) to estimate f(3.1, 8.8). y2+7 (Use decimal…

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