y z lim (x,y,z)>(0,0,0) x² +4y² +9z .2

Q: find the absolute maximum and minimum values of ƒ on the region R. ƒ(x, y) = 4xy - x4 - y4 + 16 R:…

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Q: If f(r, y, z) does lim f(r, y, z) exist? %3D 1² + 2y? + z² ' (z,y,z)¬(0,0,0)

A: To find its limit we have to first convert the function into polar form.

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A: Given, the function f(x, y, z)  = e-xy cosz, and we have to calculate the partial derivative fx, fy,…

Q: (a) Find the solution of the limit using polar coordinate system. x² + y² x² + y2 lim(x.y)→(0,0)

A: Solution:Given to the find the limitlim(x,y)→(0,0)x2+y2x2+y2In polar co ordinates x=r cos θ   and y=…

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A: given curves are                                                  x2+y=6y=xy=-3

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Q: TEANUCOGl b) Given z = f (x – y, 2x – 2y, 3x – 3y). Show that - dz dz = 0. he

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A: Dear student, since you have posted multiple questions, as per our policy we will answer first…

Q: CALC I | FIND AZTA of RELDON BOUNDED By Y=e, y=e^, x=1, x=2

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Q: Utt Urr 100, x > 0, t > 0. u (x, 0) = u (x, 0) = u (0, t) = 0 lim u (x, t) = 0, x → 00

A: 1. Laplace transform is an integral transform that converts a function of real variable t to a…

Q: Use polar coordinates to find the limit. [Hint: Let x = r cos(0) and y = r sin(0), and note that (x,…

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Q: Q.No (2) Use the limit definition to find partial derivative of f(u, v,w) = u² – nuw + (n + 1)v² –…

A: To find -

Q: y; Let it be described implicitly as a function of x and z by the following equation: eXZ – sin(TXZ)…

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A: 7

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A: answer

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Q: ∫∫R(x^2)sin(xy)dydx; R={(x,y)l(0≤x≤π),(0≤y≤1)}; R=limits

A: Explanation of the answer is as follows

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A: Given function is, fx,y=xyx2+y2;                x,y≠0,00;                                x,y=0,0…

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A: We have z=xy=s+t2s2-t By differentiating z with respect to s,…

Q: container is formed by revolving the region bounded by the graph of  y = x2 , and the x-axis, 0≤ x…

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Q: (a) ze'u lim (x..)(-1,0,4) 6z+ 2y-3z (b) I-4y lim (r,v) (0,0) 7z+ 6y

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Q: Higher Partial Derivative z=2x²-3xy +4y²; d²z 1. oxoy² 3. z+x³ − ln(y³ +x³)= 0; - a²z axoy 0³ z…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

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Q: 10 Find div F and curl F if F(x, y, z) = xz°i+ 5y"x²j+ 4z?yk. div F= curl F=

A: Solution:

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.