Let f(x, y) lim (x,y) → (0,0) = ● 3xy² 3xy² x² + y² Compute lim f(x, y) by first converting to polar coordinates. (x,y) →(0,0) = lim r0 (3r-cos (theta)) (r - sin( theta))² (r.cos(theta))² + (r.sin(theta)) ² Note: In the first blank, enter the function in polar coordinates. Type the word theta to enter 0. Be sure to use a * when you write something like r * cos(theta) 0

Q: f(x, y) = xy², (3,-2). alru) — sin(ru) (9) T

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Q: * Find (fzyx) for the function (f = sin(xy)* .cos(yz)* cot(xz) ) B) zycos(yz)-sin(yz) O A)…

A: Given: f=sinxycosyzcotxz To find: fzyx

Q: Use Green's Thoerem to evaluate F dr. where F(r, y) = (-3Vx² + 2, 7 tan '(x)) and C is the triangle…

A: We have to evaluate by Green's theorem.

Q: If f(z) is analytic function expressed in polar form, show that: (sin + icos) of ᎧᎾ f'(z)=(cos- i…

A: To show that the derivative of an analytic function f(z) in polar form is given by:we'll use the…

Q: - Let f(x, y) =sin(x y − x − 3y+3). (vi) Which of the surfaces below is a graph of this function?

A: Given .This can be rewritten asOn the xy−plane, , if  gives us hyperbolas on the xy−plane.

Q: Bluetop Cab charges $3.20 for the first mile and$1.35 for each additional mile or part of a mile.

A: Given: Bluetop Cab charges $3.20 for the first mile and $1.35 for each additional mile or part of a…

Q: Consider the function z= = f(x, y) = sin(x - y). (a) Plot the cross-section where the graph of z =…

A: Since you have posted multiple questions with multiple sub-parts, we will provide the solution only…

Q: f(r,t) = cos(3r) exp(4t) %3D fi(x,t)+ frz(x,t) = f(r,t) %3D

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Q: Let h(x, y): = x5 + y sin²x x² + y² 0, if (x, y) = (0,0) if (x, y) = (0,0) (a) Show that h is…

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Q: Find f, and f, and evaluate each at the given point. (x, y) = arctan), (2, -2) %3D ,(x, y) = ,(x, y)…

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Q: Let f(x, y) = x sin ry. Find: fyy (x, y) fyz(x, y)

A: f(x,y)=xsinxyfx=sinxy+xycosxyfyx=xcosxy+x(cosxy-xysinxy)=2xcosxy-x2ysinxyfy=x2cosxyfyy=-x3sinxy

Q: Let C be the curve defined by 7(t) = (2+2 sin(t), 3 – 2 cos(t)) for 0 <t< L (e + 4z) dz + (2zye" +…

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Q: Which of F(x, y) = (-y, x) and G(x, y) = (y,x) is conservative in R2 and why? If again F(x, y) =…

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Q: Consider the curve C shown in the attached figure, which is the intersection between surfaces S, and…

A: To parameterize the curve which is the intersection of the below curves in the first octant.…

Q: Let C₁ be the straight line from the point (1,0) to the point (0,1) in Figure 1. Let C₂ be an…

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Q: Img(:)=v(x.y) and g(-)=g: v(x, y) = 2x-2ry+sin xsly and g (0)=-1.

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Q: Consider the function z = f(x,y) = sin(x – y). (a) Plot the cross-section where the graph of z =…

A: Given z=sinx-y. (a) The xz plane is given by y=0. We get, z=sinx. This is just the sine curve in the…

Q: F(t) = %3D a. elliptical helix |F(t) = b. conical helix %3D ]F(t) = c. line d. circular helix…

A: We will use standard parametric form of these curve to match   For circle x = a cos(t) y = a sin(t)…

Q: Let h(x, y) = x5 + y sin²x x² + y² 0, { 25 if (x, y) = (0,0) if (x, y) = (0,0) (a) Show that h is…

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Q: f(x, y) = xsin²y + y² cosx, Find fxy a. sin² y - y² cosx b. 2xsinycosy-2ysinxcosy c. 2sinycosy -…

A: We need to find fxy.

Q: sin(xz – 1) In(6+ 3xz + 4yz) = 0 determines z as function of x and y in a neighbourhood of the point…

A: Claim: at (x,y)=(1,1) for the equation  Take partial derivative with respect to x Substitute…

Q: 2-g(%,y)%3D플-플 * at (VT ,1)

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Q: ) Given "-(3) - in R² 1. Parametric Form of xParametric Form of y Domain of Range of / y- Vi

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Q: For F(x, y,z)=(6xsin y+10xz' )i+(3x cos y-4ye"-2y ze" ) j+(-2y'e* +15x²z² )k , find | a function f…

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Q: Does f(z)=z/(sin z)^2 have a pole of order 1 or 2 at z=0?

A: f(z)=zsin2zFor the poles first we look at the zeros of the denominatorat z=0 We know sin(z) has a…

Q: Please

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Q: f(x.y) = arcsin( x? +y² –1)+/x² +y² -1 fonksiyonunun tanım kümesi aşağıdakilerden hangisidir? (a)…

A: From the given information. The function f(x,y) is as follows. fx,y=arcsinx2+y2-1+x2+y2-1