f(r, y) = 3y + 5a² + In (x² + y² – 9) + In (2² + y² – 9)

Q: xy f(r, Y) = 7² + y²

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Q: 2. Prove that the function f : R? → IR defined by f(x, y) = 1- a2 – 4y? is neither injective nor…

A: Given the function f:ℝ2→ℝ defined by fx,y=1-x2-4y2

Q: Find the interval that the fullowing function is continous at In (9 -x) %3D A. [I,3] BL) (3,3) (1,3)…

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Q: Define f : R2 → R by letting (y² – x)² (y4 + x²) f(x, y) = if (x, y) # (0, 0), and f(0,0) = 1. ||…

A: The given function is f:ℝ2→ℝ defined as: fx,y=y2-x2y4+x2if x,y≠0,01if x,y=0,0 Claim: The given…

Q: Show that if u =x - y and v =r+ y, then for any continuous f, e-2s* f(x - y,x + y)dydr = || (a+n)e-…

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Q: Determine the set of points at which the function is continuous. f(x, y, z) = 4x + 7y + z D- {x, v.…

A: We know that a function g(x)=sqrt(x) is continuous for all x such that x is greater or equal to 0…

Q: Let f(x, y) = - 4xy² – 2x² + 8y². Find and classify the critical points of f.

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Q: Find c such that the function ( a2 – 4 x c 4x – 8 x > c is continuous everywhere. c =

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Q: For the function f(x,y,z) = In (10x + 7y + 6z), find fy, fy, and f,.

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Q: Please

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Q: Let z = f(x, y) = 5x – x³ + 2xy – y². - Find and classify all the critical point(s) of this…

A: Differentiate the function fx,y=5x-x3+2xy-y2 partially with respect to x and y, to obtain fx and fy.…

Q: Let f be a differentiable function of one variable, and let f(p), where p = (x² + y² + z²)'/2. Show…

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Q: Consider the function f(x,y) defined on the domain D f(x, y) = 2x + 3y – a² – y? - оn the domain, D…

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Q: For the function f(x,y,z) = In (5x + 7y + 1Oz), find f,, f, and f,.

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Q: Show that the function is differentiable by finding values of ε1 and ε2 as designated in the…

A: Given, the function f(x, y) = 5x – 10y + y3, we have to show that the function is differential by…

Q: Let h: R → R be a continuous function on all of R. If h(x) T, prove that h(Tt) <0.

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Q: At what points is the given function continuous? f(x, y) = V9x + 6y O All (x, y) such that x + y 2 0…

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Q: Let f(x,y)=3x2-2xy+y2-8y  Find the absolute extrema over [0,1]x[0,2]

A: Consider the given function fx,y=3x2-2xy+y2-8y First, find the partial derivatives of the function…

Q: of and dy For the function f(x,y) = In (8x + 9y), find - - of

A: partial derivative of two variable functions

Q: For what value of b is

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Q: Let h: R → R be a continuous function on all of R. If h(x) I prove that h(Tt) <0.

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Q: 2.) Determine the set of points at which the function is continuous. а. F(x,у) — 1+x²+y² 1-x2-у? ху…

A: Here, to find the set of points at which the function is continous.

Q: Suppose that  ff"' is continuous and f'(c)  =f"(c) =0 , but f"'(c) &gt;0. Does f have a local…

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Q: What value of c makes the following function continuous at (0,0)? f(z, y) = C, x+ y³ +2, (x,y) +…

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Q: Find c such that the function f(2) = { S2? – 3 x c is continuous everywhere. C =

A:

Q: Let f be of the class C" in the interval [a.b] and let c be an interior point of this interval with…

A: We have to Show that if f"(c) &lt;0 then f has a local maximum at x=c. We know that A function f has…

Q: Find the domain of the following multivariable functions b. f(x,y,z) = x/y+ In (z – 1) c. f(x,y,z) =…

A: Solution:Domain: The domain of a function is the set into whcih all of the input of the function is…

Q: Let f(y) be the function such that S f(y)dy=y In (4 + 9y²) + C. 1 Evaluate f 4x f(x² + 1)dx.

A: Calculation of Required Value.

Q: Consider the following function: f(x, y) = {xy cosy/3x2 + y2     if (x, y) 6 not equally to (0, 0)…

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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: sketch the given function and determine whether it is piecewise continuous on[0,∞).

A: The given piecewise function is The graph of the function is as below:

Q: Find f, and f, for f(x,y)=y In (3x +4y). fx fy

A: When the partial differentiation is done with respect to a specific variable, then all other…

Q: Which of the following interval is f(x) = O (2, +∞0) O [2, +∞0) 0 (-∞0, +∞0) ○ (0, +∞) 1 Vx…

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Q: |Consider the function f with domain (-2, 0): 3|1² – 1| 21² + 2r – 4 if – 2<1<1 f(z) = if x = 1 3 if…

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Q: Let h: R R be a continuous function on all of R. If h(x) Tt, prove that h(t)<0.

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Q: Answer the following questions a- Show that fxy = fyx for the function f(x, y) = ().In(x) aw

A: We need to show fxy=fyx. As per Bartleby's guidelines we can solve one question from multiple…

Q: Find the Wronskian for the set of functions.{ex, e−x}

A: Given set of functions ,f1=ex &amp; f2=e-x

Q: Consider F(x,y)=(4x^3+4y)i+(4x+6y^2)j Show that F is conservative, and find a function f such that…

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Q: find the domain of the following function and show it in the xy plane. f(x, y) = In(9 – x² – y²) + 1…

A: Given function  f(x,y) = ln(9-x2-y2)+1x+y-3

Q: Find c such that the function 10 I C - is continuous everywhere.

A: A function f(x) is said to be continuous at a point x=a if limx→af(x)=f(a). That is, a function f(x)…

Q: Let f(x) = V31 – x. Compute f'(6) using the limit definitic f'(6) = %3D Find an equation of the…

A: Given: f(x)=31-x

Q: Determine the value of m such that the function 5 + 5 y fi^ - ^ - f(z, y) = is continuous at (0,0).

A: Given that function s continuous at (0,0). We need to find the value of m.

Q: Let f(r) = V7 2. Compute f'(3) using the limit definition %3D f'(3) 3D Find an equation of the…

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Q: 3. Show that there does not exist a non-constant continuous function f : R2 → R such that f(x, y) =…

A: Given:- f: R2→R

Q: Determine the set of points at which the function is continuous. a) f(x,y) = ln (a²² + y² – 4)

A: Given function is                                                              f(x, y)=ln(x2+y2-4)…

Q: the function 2x4jwhen x²+y°+0 Prove that h (a,y) %3D Oj when x=y=0 epect is Variables Lontinuous…

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Q: 36. f(x, y, z) = vy – x² In z

A: We have to find the point where the given function is continuous.

Q: Let f be a C' function on the line, and let g(x) = S f(xy)y² dy. Prove that g is a C' function and…

A: f ∈ Cn  means f is atmost n times differentiable