3 Q7- Let fw=ex-y, Find a fun ction y =gcW So that f. 9) (x) = X+ 2 .

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

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Q: The domain of the funsfon f(x) te 9) E2,21, or equivalenfly,t243 C) [4,00, 0r )(00,4),or…

A: This question can be solved by applying the concept of existence of function at various points on…

Q: 2. If f (x) = Sn* et? 0, dt, find f'(x) V2t+sect

A: The solution is given as

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 the D.f ofr (x, y) = (x² – y)' at Po(3, 1) with

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Q: 1 Q9: Let f(x) = cosx x + 3 then find all critical points. 2 -

A: A critical number C is a number in the domain of 'f' for which eitherf'c=0 or f'cdoes not exists.…

Q: 2. Let f(x, y) = In(x² + y²). Show that fre + fyy = 0. %3D

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Q: 1. If f(x, y)=3x' cos y– y sin x– 2.x In y- yln x-4x²y, find ôf ôf d²ƒ _ô²ƒ

A: According to question given thatf(x,y)=3x3 cosy-y2 sinx-2x ln(y)-y ln(x)-4x2y

Q: 4. Integrate the function f(z) = z² + 2z from z = -i to z = 1 in two ways, once along a straight…

A: The objective is to integrate the function fz=z¯2+2z from z=-i to z=1 in two ways, Once along the…

Q: 2. Show that 4=x i+y°j+:'k is irotational.

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Q: Q2: Expand f(x,y) = [sin (x y³)]² about (5, 1).

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Q: Q1: If Z = f(x·y) + g. Prove that x² - Zxx + x· Zx = y² · Zyy + y Zy. %3D

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Q: 2z Forz> 0, 순(/"m(P + 1) a) In (t³ + 1) dt For x > 0,

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Q: 2. Find frxz for f(x, y,z)= z² e³xy

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Q: Q2: Let f(z) = z² is f(z) satisfy Cauchy-Riemann equation ?

A: The general form of a complex number is given by z=x+iy, where x,y are two real numbers and i=-1.…

Q: (8) Suppose f(x, y) = -x + y², x = s² +t°, y = 2s – 3t. Compute f, when s = 1 and t =-1. %3D

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Q: x - y -2x Prove by definition that for f(r, y) fy(x, y) = %3D x+ y' (x+ y)2

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Q: 4. a) Find an approximation for f (x, y) = at the point (1.97,1.02). V10-r-5y b) Check Euler's…

A: (a) Approximate f(x,y)=410-x2-5y2 at the point (1.97,1.02) (b) Check Euler Theorem for…

Q: If f* f(t) dt O 6 1 O -4 divergent = 20x √4x²+21 ∞ -4, then f(t)dt is X

A: Given

Q: . Let f(x,y) = 10xy^4 +x^5y^2. Find fyyy.

A: We have to find solve

Q: Find D,y, given y = 3e" (2x – 5)*. D.y = 3e [4(2x– 5)'(2)]+(2r-5)'(3e") = 24e" (2x – 5)' + 3e"…

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Q: Find solution of an equation x X f(x) 1 1.0000 1.25 0.8000 1.50 0.6667 0.5714 1.75 2.0 0.5000 Using…

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Q: O Find all second order derivati ves for f(x,y) = Cos(2x) - x²e5Y + + 3y2

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

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Q: If A(x)= f(t)dt is increasing on [0,10], then f(x) must be increasing on [0,10].

A: Given,A(x)=∫0x f(t) dt

Q: 2 3 tegral of the function xy d by x = 0, y = 0, z = C %3D %3D (2(5)

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Q: 3. Evaluate f 2xdx + (y + 2)dy along the rectangle with vertices (0, 0), (0,3), (3,3) and (0, 3).

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Q: 6) If y=x² +1+ f dt , prove that y"= 2 - x2

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Q: 8. Find the work done by F = (x² – y,x) along C:7(t)=(2cost,2sint) 0<t<2n : a) Without Green's…

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Q: 7. Let f(x, y) = 10x³y* + 21xy². Find fyyy. .3,4

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Q: Let f(x, y) = ln (3x + y2). Show that fxy = fyx

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Q: In x 2. Use a local linear approximation of f(x) = 1+x² to estimate In (0.9) 1.81

A: Given - fx=lnx1+x2 To estimate ln0.91.81 using a local linear approximation of fx. Here we will use…

Q: For o fynction t4 suppose that Suppose and and Which is true for the points P(l,D and QC1,2) where…

A: Given that , For a function f(x,y): fxx=x2 , fyy=y2 ,  fxy=2 Critical points of f(x,y):  P(1,1) and…

Q: (b)Assume that f(x) is a function of the form -x-1; when -T < x <0 f(r) = when 0 <r < T Prove…

A: For the solution of the problem follow the next step.

Q: 9. f(x.y. z) = In(x + 2y² + 322); P(-1, 2.4): u = -i- j - k

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Q: Find the zeYo k its ovdev for Sunction f2)=1-Ti + Z+ e.

A: Given the function, f(z)=1-πi+z+ez. Now, in order to find the zero of the function f(z), we will…

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: Q2- If Z = f(x, y) = sin(x³y5) Find fyy and fyx

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Q: 19 Suppose that Ts Cx) centered at 2 for f (x) is gicn by Ts Ca):345Ca-2)+5 Cx-2)?ょ2x-2)+(x-2) Than,…

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Q: -2 In(x) Consider the function f(x, y) 3y

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Q: Suppose fn → f and the functions fn all satisfy the Lipschit condition |fn(x) – fn(y)| < Mx – y| for…

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Q: what is the antiderivative F(x) 0f f(x)=3x^((1)/(2))-x-1that satisfies the condition F(4)=0 A,…

A: Given that:f(x)=3x1/2-x-1, F(4)=0

Q: If f(x, y, z) = In(x³ + yl² + 2®) + V (x12 + y6 + 23), then find fr, fy and f; at (1, 1, 1).

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Q: 3.2 Let f(x) = Approximate the integral x4 x L f(x) dx using the Trapezoidal rule with n = 4. -2

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Q: (ii)If y=(x+Jx* +1. prove that y'= Vx +1

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Q: 2. Evaluate f(x) = e3x + 2 at x = -1. Round to the nearest thousandth. %3D %3D f(-1) = ...

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Q: Prove that fxy fy x for the following: %3D f = e + x Lny + y Lnx f = xy 2 3 + xy4 f = Ln ( 2x + 34)

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Q: 3- Prove that (y" f(x)) = "(x)y) = fy where y E Rm and f: R" → R™ %3D %3! ax ax

A: The objective is to prove that  ∂∂xyTfx=∂∂xfTxy=fxTxy where y∈ℝm  and  f:ℝn→ℝm