A) f(x,y)=z²-y. Sketch 4 level curves of f(x, y). B) Evaluate the following limit or show that it does not exist 7zy lim (z.) (0,0) 3x² + 5y2 C) Write a function f(x, y) such that the domain of f(x, y) is D = {(z,y) | 2² ≥9-y²}. Also provide a sketch for the domain.

Q: ててーて ー|ト 5 +エ-6 9-ズ 9 FIND all Polnts 9t which f(x) IŠ dis Continuou b) find lim fa). メーウと ) Find…

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Q: .2 - (a) lim x + y (2,y)-(1,1) xy y+4 (b) y # -4, x 4 x lim (7.y)-(2,-4) x2y - xy+4x2- 4.x' 1 a+y-4…

A: To calculate limits by arranging fractions:(a) lim(x,y)→(1,1) x2-y2x-y=lim(x,y)→(1,1)…

Q: 2] Show that the limit does not exist by considering the limits as (x, y) → (0, 0) along the…

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Q: a) lim W→0 f(3+w)-f(3) W y-f(x) Fig. 10 b) lim h→0 4 ƒ(4+h)-f(4) h c) lim S-0 ƒ(5+s)-f(5) S

A: The given graph of  shows the function is discontinuous at .The given limits show the derivative of…

Q: 5. Find the limits: a) limg→0 4 – Vx + 16 Vz – 3 b) limz→9 z - 9 t +2 c) lim→-2 |t+2|

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Q: Find the limit lim (a,y) (-45,9) xy cos(x + 5y) (Enter 'DNE' if the limit does not exist)

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Q: 1.a) Find the limit: lim 2eti + 6e-tj-4e-2tk t→ln2 (simplify, exact value) b) Find the limit: lim…

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Q: Find the limit (enter 'DNE' if the limit does not exist) 1) Along the x-axis: 2) Along the y-axis:…

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Q: If the limit lim (x,y)→(0,0) F(x, y) = 0 along the path of the form y = kx for any real number k…

A: Follow next step

Q: 2.a?y Using paths, show that the following limit does not exist. lim (x,y)→(0,0) 3x4 + y?

A: According to the given information, it is required to show that limit does not exist.

Q: Determine which of the given limits does not exist 2y² 2x² - y² A. lim (x.v)-(0,0) x²y (x.v)-(0,0)…

A: determine the limits

Q: Use the graph to determine the limit. (If an answer does not exist, enter DNE.) y 4 (2, 3) C = 2 4 6…

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Q: 4. Determine the limits: a) b) 4x²-8xy lim (x,y)-(2,1) (x²-xy-2y², lim (x,y) → (0,0)…

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Q: Find the indicated limit by using the limits lim f(x, y) = 5 and lim g(x, y) = -4. (x, y) - (a, b)…

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Q: Find the limit of  lim(x,y)→(0,0) (x^2 + y^2)/(sqrt(x^2 + y^2 + 1) − 1 rationalize the denominator

A: To find the limit value :

Q: 5. Use L'Hôpital's rule to obtain the following limits: (a) lim r²Inr

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

Q: Let f(a, b) = a/ (b − 1)^2 . a. Describe the domain of f. b. Sketch the level curves of f…

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Q: Question a) b) Consider the function f(x, y) = Find the domain of f. Show that the limit does not…

A: Domain Area of control,   means area where function is defined.  For the given function we have to…

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A: (a) First draw the figure,   Let r, h, V be the radius of base, height and volume of the cylinder…

Q: 5) Find the following limits: E) lim ¹ x-0-3x D) lim y-0 sin(3y)cot (5y) y cot (4y) 7x3 X-00…

A: we find the limits .

Q: Question a) b) 2xy Consider the function f(x, y) = 4x²+5² Find the domain of f. Show that the limit…

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Q: 7. −ydx + (x + √xy)dy = 0

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Q: 1. a. Describe the level curves of the function f(x,y) = %3D x* + y b. Show that the limit lim (2,y)…

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Q: (2)(-_ A) f(x, y) = 2²-y. Sketch 4 level curves of f(x, y). B) Evaluate the following limit or show…

A: The level curves of a function f of two variables are the curves with equations f(x,y) = k, where k…