10. Evaluate the following limits (Aşağıdaki limitleri değerlendiriniz): x² - y² ii) lim (x,y)+(0,0) x² + y²¹ i) lim (x,y) → (In 2,0) iii) lim (x,y) → (0,0) x cos( Y

Q: d) Let the function: f(x, y) = 3, < 0, Find the following limits: (i), lim (z.y)-(3,-2) f(x, y) ,…

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

Q: lim If (2,y)(0,0) f(x, y) = 0 then lim f(x, 0) = 0. T→0

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Q: 3) lim (x² + y²)' 1.

A: Given: limx→0y→0x2+y2x

Q: Find lim (x,y,z)-(0,0,0) x²+y2+z4 xy+yz?+xz2 if it exists, or show that the limit does not exist.

A:

Q: 2. Evaluate lim (X,Y,Z) TT10,37 -२५ ze cos(2x)

A: limx, y, z→π, 0, 3ze-2ycos2x

Q: 1 I. x² +y³).sin- x³ +y³ lim (х, у) -(0,0)

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

Q: Find each limit f(x, y) = √y( y + 1)

A:

Q: lim (4 + (x + y} ) In(x² + y)) (х.у) - (0,0)

A:

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: If f is continuous for all nonzero x and y, and f(0,0)=0, then lim f(x,y)=0 as (x,y) approaches…

A:

Q: Let Find f(x, y, z) = x³y + x²yz x² + y6 + z4 lim (x,y,z)→(0,0,0) f(x, y, z) if the limit exist or…

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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: 1. Let Find f(x, y, z): = r³y + x²yz x² + y6 + 24 lim (x,y,z)→(0,0,0) f(x, y, z) if the limit exist…

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Q: Calculate the limit if it exists

A: Given that:lim(x, y)→∞2xy+6xx2+y2+6y+9

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: (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…

Q: Do the following limits exist ? If yes, find their value xy lim (x, y) (0,0) x² + y² xy lim (x,…

A: We are given the functions in two variables. a fx, y=xyx2+y2 b fx, y=xyx2+y2 c fx, y=xyx2+y2 d fx,…