x² sin +y f : R² → R, ƒ (x, y) = %3D x + y

Q: Given D = exp (-x) siny ax – exp (-x) cosy ay, the divergence of D is %3D а. 1 b. 3 С. 2 d. 0

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Q: Given a function f(w, x, y, z) = y ln(wx) + (+1) tan z, which of the following is not part of the…

A: follow next step

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

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Q: define y as a differentiable function of x,  find the value of dy/dx at the given point. 25. x2 + xy…

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Q: 10. Find the linearization, L(x,y,z) of the function f (x, y, z) = e* + cos(y + z) at Po (0,",").

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Q: Find the linearization of the function f (x) = x at x = 1. a lal sin (a) L (x) Using this…

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Q: Evaluate lim (csc a) V. x0+ Let f(x) = Va + le¬*. 1. Find the local linear approximation of f at xo…

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Q: A function f : R? → R is given by f(x,y) = y² + 2x² – x²y. Find and classify its critical points.

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Q: 4. If f is a differentiable function of x and y with w = f(x, y), x = r cos 0 and y = r sin 0, show…

A: Given: w=fx,y, x=rcosθ, y=rsinθ If w is a multi variable function w(x,y,a,........z) thus the…

Q: Find the linearization L(x, y) of the function f(x, y) at P0 Then find an upper bound for the…

A: We need to determine the linearization of the function: f(x, y)=xy2+ycosx-1 at P01, 2 over R:…

Q: find ∇f at the given point. ƒ(x, y, z) = (x2 + y2 + z2)^(-1/2) + ln (xyz), (-1, 2, -2)

A: Given function is  Firstly, we find all first order partial derivatives of f

Q: define y as a differentiable function of x,  find the value of dy/dx at the given point. 25. (x3 -…

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Q: . Find all values of the constants m and b for which the function S sinx, y mx + b, x 2T is a.…

A: To find all values of m and b for which the function:   y=f(x)  =  sinx    x<π…

Q: a sin (), it (, u) + (0, 0) x²+y? 2. Determine if a function f : R² → R defined by f (x, y) = 0, if…

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Q: The linear approximation at x = and where B is: 0 to 1 X is A + Bx where A is:

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Q: Find the (absolute) maximum and minimum values of f(x, y) = sin x cos y on the square R = {(x, y)|0…

A: Given,            f(x, y)= sinxcosy                    (1) on the sqaure             R=x, y| 0≤x≤2π,…

Q: Find the linear approximation of the given function at (0, 0). f(x,y) = sqrt(y+(cos(x))^2)

A: The given function fx, y=y+cos2x The linear approximation in 2 variables is given by Lx, y-fa,…

Q: Find the linear approximation of the function at the given point: f(x, y) = 2 sin x – 3 cos y at (0,…

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Q: Where is the function f(x, y) = e' arctan (VI+In(x+y)

A: In this question, the concept of continuity is applied. Given function is fx,y=etan-11+lnx+y

Q: The harmonic function for f(z) = u(x,y) + iv(x,y) to be analytic are:

A: Given that: f=u+iv

Q: The tangent line to the curve y=f(x) is horizontal at where X = Xo f f(xx) = 00 A O f(xo) = 00 .8 O…

A: The tangent line to the curve y=f(x) is horizontal at where x=x0 if

Q: Find domain of following functions In(e*+e) arctan(x+y) x² – y? а. f(x, у) — b. f(x, y) = - Vx - y…

A: Domain of a function is the set where the function is well defined. Thus, we check the points where…

Q: Find the linearization of the function f (x)= x³ at x = 1. qb |a| sin (a) L (x) = Using this…

A: Given, fx=x5 We know that, If we have a differentiable function f defined near "a" the linearization…

Q: I sin () if (r, y) # (0,0) 2. Determine if a function f : R2 R defined by f (x, y) = 0, if (r, y) =…

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Q: The function f(z) =e² is: contiuous in C discontiuous in C Ou(x,y) =e*cos(y) Ou(x,y) =e*sin(y)

A: The function f(z)=ez the given function is continuous.

Q: Assuming 9x° – 5y - 4xy = 0 defines y as a differentiable function of x, use the theorem dx - to…

A: Given: 9x3-5y2-4xy=0 We have to calculate dydx(1,1) by the given formula.

Q: Show  that the function Z =1/2(eysinx - e-ySin(x) satisfies the La Place’s equation  =0

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Q: l. sin (x) dA where D is bounded by y cos x, 0 <x < /2, y = 0, and x = 0.

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

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Q: (i) Find the linear approximation of the function f(x, y) = 1 - xy cos πy at (1, 1) and use it to…

A: Here, the given function is: f(x,y)=1-xycos πy To find the linear approximation of the function. For…

Q: Given the function f(x, y) = y + e**y, where x = In(s) and y = sin(s2t), find the partial %3D af af…

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Q: b) Find the maximum and minimum values of the function u(x, y) = e' cos x throughout the region {(x,…

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Q: The function h(x) = sin væ² + 1, x E R is continuous on: O R\{-1} O R\{-1,1} O R\{0} O R O R\{1}

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Q: Given F(x, y) = (sin y + e*, x cos y) and C: x=t, y=t(3 —t), 0≤t≤ 3. (a) Show that F is conservative…

A: Given : F(x,y)=sin y+ex,xcosy C:x=t, y=t(3-t), 0≤t≤3. To show:  (a) F is conservative and find a…

Q: Determine the numerical value of dF of the function F(x, y) = e-3y cos(nx) given that X = 1, y =…

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Q: Find the linear approximation L(x) to y = f(x) near x = a for the function. f(x) = 1 a = 3 L(x) :…

A: The solution are next step

Q: Ql: f(x.y)-y cos xy over the rectangle 0sxs , 0 sys1

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Q: Let f (x,y) = sin(xy) + x² ln(y). fyx at (0,) is equal to: %3D А. 33 В. О С. 3 D. 1

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Q: xY 2. (a) Prove that the function f(x, y) is differentiable everywhere in its do- %3D x2 + y? main.

A: Solution is given below:

Q: Find the antiderivative F for f(x) = | sin z|, -T <x <0 satisfying F(0) = 1. (1) F(x) = - cos x – 1…

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Q: 1. Find if the function is continuous in the given points (x, y) = (0,0) (x, y) = (0,0) x + y = 0 x…

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Q: Show that the p.d.f. of Z is given by g1(r) = e-1(+A)cosh(vAx), x > 0, where cosh(2) = }(e² +e=*) is…

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

Q: 4. Given f(x, y) = arctan(x + 2y). Find the local linear approximation of f at (1,0) and use it to…

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Q: Find the linear approximation L(x) to y = f(x) near x = a for the function. f(x) = sin(x), a = 2…

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Q: Tir Find the general function M(x, y) so that (xM(x, y) – y) dx + (sec² y – ) dy = 0 is exact y-ln…

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Q: implicitly dx

A: Solved below

Q: Find the linearization of the function f (x) = =° at z = 1. L (1) = Using this linearlization, ƒ…

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.