Describe the long run behavior of f() = (x – 4)(x + 3)°(x – 1)²: As a - 00, f(x) → ? As x 0, f(x) → ?

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…

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Q: Suppose that g is a continuous function. Find the general solution of y" – y = g(t).

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Q: If f(x, y) = y° cos(x) – x³ In(y), find the second partial derivative ду дх .A ² f ду дх 3x2 -2y…

A: Calculate partial derivatives

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A: Given: f(x, y, z)=4xy-z2, x=4r cosθ, y=cos2(θ), z=7r

Q: Example H·W: for f(x,y) = cos(xy) - x3 + y compute fxyy, fxxyy

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Q: 1-Find the mixed partial derivative: w = e* +x In(y)+y ln(x)

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Q: If F(x,y) =ln (x2y - xy2), find the partial derivatives Fx (3,2) and Fy (3,2)

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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: (5) The partial derivatives of f = f(x, y) are f. = 6(x² – 1)(y + 1), - fy = 2.r(x? – 3). - Find all…

A: Disclaimer-Since you have asked multiple questions, we will solve the first question for you.  If…

Q: Q3:Find all the second order partial derivatives of the f(x, y) = 2x*- 5x'y3-y

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Q: Q2. Find the second order partial derivative of F(x.y) = x³+ x°y°- 2y² w.r.t. x at (2,1).

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Q: If f(x, y, z) = 12ry - 2yz - 6zx + 7, then the first order partial derivative f = O - (2y – 6x) (2y…

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Q: If f is a function of three variables that has continuous second-order partial derivatives, then…

A: This question  is based on a simple theorem

Q: 8. What is the relationship between a and b so that F(x, y) = (ary, 3ax + bry) is source free?

A: That's easy. Have a great day!!!

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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…

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Q: If f is a function of x and y such that fxy and fyx are continuous, what is the relationship between…

A: Function: fx and fy are continuous function. Let us choose f(x,y)=x3y3+πxy Here fx=3x2y3+πy…

Q: Find the linearization L(x) of the function at a. f(x) = sin(x), a 6

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Q: 1- Find the mixed partial derivative: w = e* +x In(v)+y ln(x)

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

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Q: 1. Use the definition of partial derivative as the limit of a difference quo- tient in order to…

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Q: Let f(x, y, z) = 6xy- z, x = 3r cos(0), y = cos (0), z = 3r. Use the Chain Rule to calculate the…

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Q: Find the linearization of the function f (x) = x° at z = 1.

A: Given, f(x)=x6

Q: Find the linearization L(x) of the function at a. f(x) = sin(x), a =. 3 L(x) =

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Q: Find all second partial derivatives of the function f(x, y) = In(3x? + 5y).

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Q: lim, f(x)= 0, then | f(x)dx diverges

A: Statement:  limx→∞ f(x)≠0,  then ∫1∞ f(x) dx   diverges.

Q: Find the four second partial derivatives of the following function. f(x.y) = In (7x2 +2y? +7)

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Q: 2) Let f(x, y) = x sin(2y) + 5y¹. Find fyyyyyyyyyy (x, y) (10 partial derivatives), explaining how…

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Q: Find the linearization L(x) of the function at a. f(x) = sin(x), a = 3 L(x)

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Q: Use the Chain Rule to calculate the partial derivative. Express the answer in terms of the…

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Q: If ƒf (x) =¸ (A) (B) Sº sec²x 1+elanx In (secx) √✓ 1+tan²x tanx 1+e sec ³x tanx 1+e 1+1² tanx…

A: Using Leibnitz integral rule.

Q: Let f(x, y, z) = 8xy – z², x = 7r cos(0), y = cos²(0), z = 3r. Use the Chain Rule to calculate the…

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Q: 10. Use the Chain Rule to find the indicated partial derivative if ax F = Vu? + v2 + w², u = xe, v =…

A: F=u2+v2+w2To find ∂F∂x

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Q: Find the partial derivative with respect to z of the function (3a – 2)e2y-5 In(-5z - 1).

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Q: (or axay дудх Calculate the second-order partial derivative of f(x.v) = xy with respect to x and y,…

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