a2f b- For the following functions prove that ax2 ay2 1- f(x,y) = e-2y cos 2x %3D f(x,y) = In/x2 + y² %3D

Q: S dg = f dg cos 0 where, cos e = VR+xa GS Rd0 x J (VR² + x²)²VR² + x² dg GS Rx de (VR2 + x²)7 GS Rx…

A: It is problem to integrate the differential 'g' within the limits. In the first step, the resultant…

Q: Find constants c1 and c2 such that F(x) = c1x sin x + c2 cos x is an antiderivative of f (x) = x cos…

A: To find constant c1 and c2 such that Fx=c1 xsinx+c2cosx is an antiderivative of fx=x cosx. Solution:…

Q: Find Ay and f'(x)Ax. For y = f(x) =- ,x = - 1.3, and Ax =0.1 x2 Ay = at x = - 1.3 and Ax = 0.1 (Do…

A: We have to find the value of given quantities from the given function.

Q: 出w-2 Verify that Wメy Wyx for the functions's T- f(xsy) = En (2X +34) fcxyy) = e+x Luy +y Lnx 2-

A: Since you have posted multiple question at a time as per guidelines we can solve only one question…

Q: 1. Let F(x, y) = 25x³ + 120x²y + 192xy? + 102y³ – 300x – 450y. Find the following: | ƏF (i). OF…

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Q: Fial dy ldx by imphieit differention. X² (x+y)=y?(7x-y) 2. Find dy /x by implicit differention. e…

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Q: 1. Use a local linear approximation of the function f(x) = Vr cos[(V2x)7] approximate v3.98…

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Q: of of H.W: Find and for the functions: Ox ду 1. f(x, y) = (xy – 1)? 2. f(x, y) = x² - xy + y? | 3.…

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Q: 25-let F(xs.2)=x-x22 @ Find VF 6 write the equution of tngent Plame to the at Paint (2,1,1). Find…

A: The given function is,  F(x,y,z)=x2y2-xz2 We have to find,  a) ∇F b) Equation of the tangent plane…

Q: Find fæxyzz for f(x, y, z) = z³y² ln(x). [Show your solution.] Select one: O O O x² 6z²y x² 2z³y x²…

A: See this solution in below.

Q: Find the valve of k so that (2y sın x cos x -y + 2 y e** ) dx - (x - sın' x + kxye*) dy 0 becomes…

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Q: Q2: Find dyidx for the following function:- (1) y = In(x + 4)-xtan (4) y =x*+1) (2) xy + x*y = x +…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: az Suppose z is a function of r and y, and csc Vr² + yz = 2"e»in z_ Solve for dz and dy

A: Given: csc x2+yz=zyesin x To find ∂z∂x and ∂z∂y.

Q: Q2. If f(x, y) = xy² + y²cosy + xsiny then a) y² - siny c) 2y + cosy a²f is дудх b) y² + cosy d) 2y…

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Q: Determine frx and fry for the function below: f (x, y) = x²y + y cos x – e*y In((y) + 7. -

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: 3 36 Consider a fumetion f whose first and second derivatives are f'(x) and f"(r) = 5/2 (1r² + 1)"/2…

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Q: Ql: If f(s,t) = s²t+ In(t² – s) find the value of a) atas Q2: For the following function prove that…

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Q: Əz Q3.If Z= f(x,y) = 4 e In(y), and x = ln (u cosv), y = u sinv, use chain rule to find : E * ди Q4.…

A: Note: We are entitled to solve only one question at a time. As the specified one is not mentioned,…

Q: 8. Let y -e=y-x²y. Find dy dxlx=1 be a function of x such that e*-y

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Q: 25. For y = f(x) = x2 - 3, x = 5, and Ax = 0.1, find Ay and f'(x) Ax. %3D

A: Given: fx=x2-3 ,x=5 and ∆x=0.1

Q: 2. | а) Determine the value of the following limits: ax? а- I. ,2 x 1+x? 1+x II. 1+x 1+x b) Find the…

A: Here we will use formula of limit limx→0sinxx=1 And chain rule of differentiation  dfgxdx=f'gxdgxdx…

Q: 2n dw at t= dt dw For the functions w = 3x - y, x cos t, and y = sin t, express as a function of t,…

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Q: a) z=-3x y² + sen(x²y) 2x c) z=-In (x y³) e) z = x²ln(2x³y) b) w=2xz-3e²xy d) z=2e²y sen(x) f) z=…

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Q: dx for 3xe dt 9-In 729 +6ln x, with the conditions 3 12, х%3D3, у-0. dt Assume x and y are functions…

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Q: Q10. Expand f (x, y) = e" cosx about up to third degree terms by using Taylor's theorem for a…

A: The given problem is to find the third degree taylor polynomial of given function f(x,y) about point…

Q: Q4: integrate the following function f(x,y) for x from z to 2n and for y from 0 to f (x, y)=…

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Q: The function y = Ce* + C2e-Sx is the general solution of a) Oy" – 3y – 10y = 0 b) Oy" + 2y + 10y = 0…

A: We have to find the differential equation whose general solution is y=C1e2x+C2e-5x .

Q: 2. Given the following function f(x,y) = x3+15x² – 20y2 + 10. %3D (i) Find fr. fy, frx. fyy. fry and…

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Q: 2. Given the following function f(x, y) = x + y? - 3x - 6y - 1. %3D (i) Find f, fy, frx fyy, fry and…

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Q: 6. Suppose f(2) is analytic in |2| 1, and f(0) = 1, f(0) = 2, compute: %3D (1) h = fe(s+ 1)2d: (2)…

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Q: Given the function y(t) with y(0) = 1,y'(0) = 3 then L(e*y") (s-1) Y(s- 1)-1 O False O True The…

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Q: A. Find the linearization of the function f(x) at the x = 0. %3D Vx+1 dy B. Let y = u20 and u = x +…

A: Applications of the diffraction, linear approximation and slope of the tangent line , total…

Q: əz Q3.If Z= f(x,y)=4e* ln(y), and x = ln (u cosv), y = u sin v, use chain rule to find : 2 ди Q4.…

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Q: [4xy + 2x] 5) Let F(x, y) =[ 2x² + 1 Is F conservative? If so, give a potential function for F. %3D

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find fa, fy, and fz. f (x, y, z) = z In (x'y cos(22)) 5.4 fy = fz =

A: topic - partial differentiation

Q: (a) express dw/ dt as a function of 1, both by using the Chain Rule and by expressing w in terms of…

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Q: 2. Show that fxy and fyx are equal for the function f(x, y) = x²y sin(x + y). %3D xy. cos(xry) + 2xy…

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Q: 16. If f(x) = 5, (;e* G +5) dt -x, then the inflection point(s) of y = f(x) is(ar- %3D 3 A) x = 4…

A: f(x)=∫0x14t4+5dt-13x4

Q: 2 Integrate the function f(2) = (z - 10i) from z = 0 to z = 5 + 5i along the line x = y.

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Q: 1. Find the most general antiderivative of the function. 4x2 +x +5 (a) f'(x) = x2 1 (c) h'(x) =…

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Q: H.W:- Prave.that.he.Maclaurinsevi.of.f(x).=-C0JA 3. (い (2n)! 2 i 5... f.(x)..co3.X.1. メ n=0

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Q: a²y azy C2 for 0 0 %3D at2 y(0,t) = y(L,t) = 0 For t > 0 For 0sxs5 y(x, 0) = f(x) = L L - x For <xSL

A: In this question, we solve the boundary value problem δ2yδt2=c2δ2yδx2the B.C:…

Q: [6 Let f(x) = |r| be approximated by sN(x) = }a0+E (an COS (") + b, sin (7). %3D n=1 Determine the…

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Q: Find the particular antiderivative F of f . f (x) = cos x ( 5sec (x)– 18/2 tan x), F (4) = 31. Enter…

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Q: Q: from the function no- kre OSxS 10 f(x) = and 1 Y dx find other wise 1-k 2- p(1 <x< 5) 3- p(-4…

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Q: of of For the function f(x,y) = In (x+ 3y), find and dx df of ду II

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Q: Consider the function f(x, y) = 3 x² y + cos(e*"). Which one of the following is correct- Oyfx-x…

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Q: (a) Prove and verify that if (x) = vx , then f (1) is 8: Vx, then f³(1) is 3/8- (b) Integrate the…

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Q: Assume x and y are functions of t. Evaluate dy / dt for 3xy - 6x + 4y 3 = -80, with the

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Q: 1. (a) Find when t = 0, if e“ cos t = (x + 1)t + 1. dt2 (Ъ) Suppose f is a differentiable function…

A: We hav to find the following conditions and we have to show the given condition