Homework 3 Due: Tuesday, November 27th 1. Find the domain of the functions a) fx,y)-32572-25 b) f(x,y)- c) f(x,y)-36- 6x2 y2 2. Evaluate the limit using the properties of the limit: 16-x2-y2-22 7xy2 lim (x,y)-(2,3) X2 + y2 3. Verify the limit using the definition: 7xy2 (x,y) (0,0)%2 + y2 4. Discuss the continuity for: 3x- x2+y2-9 5 b) h(x,y) 5. Find the partial derivatives for: 4,2 b) f(x,y)-e cos(xy2) 6. Find the slope in the x-direction and in the y-direction of the surface fix.y)-x2+ at the point (0,-1,2) using partial derivatives.

Q: 3d +4 What following laws of limits can i use for lim that equals or 1.75 d 14d2-2d+2

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Q: 2/ Find the value of the limit: lim x/*,

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A: Solve the following

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Q: Evaluate the limit 3(y? – 1) - lim y→4 5y²(y – 1)³

A: Given, limy→43y2-15y2y-13 we know LHS = RHS of given limit on y=4 function is continous on y→4

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Q: om the table, determine the following limits. I-5 1. lim I-3- I-3 HI5 4. lim I-3- r2 - 6r +9 5. lim…

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A: We have to first find whether it is determinant or undeterminant form of limit using analyticity.

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Q: Complete the table and use the table to estimate the limit. lim (2x+ 4) X→3 Complete the table…

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A: Given limit, lim(x,y)→(1,-10)y+10x2y+6y+10x2+60

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Q: Determine whether the limit exists. If so, find its value. If the limit does not exist, indicate…

A: To evaluate the given limit substitute x=3 and y=2 in the given function.

Q: 5h+4-2 Find the limit of : limħ=o

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Q: Find the indicated limit by using the limits lim (x,y) → (a, b) lim (x,y) → (a, b) f(x, y) + g(x, y)…

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Q: Evaluate the limit using the Basic Limit Laws

A: Given, limt→-1t2+1(t3+2)(t4+1)

Q: Evaluate the limits. If a limit does not exist, enter DNE. lim I-7 x + 7 |2 + æ| lim I-7 x + 7 |2 +…

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Q: date 5) lim 3メー4x?43x3 5-2 x-X3 X->0 find the limit if exists ìf

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Q: Use the properties of limits to calculate the following limit. Зху - 3 lim 2 (x,y)→(3,3) x + y +5…

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Q: Find the limit (if it exists). If it does not exist, explain why.

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Q: Determine whether or not the following limits exist (explain why or why not): x² - y² a) lim…

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Q: The limit lim (x,y) →(-2,-5) exists and is equal to -20. Select one: O True O False 25x²-4y² 5x-2y

A: The objective of the question is determine the limit existing.

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: Evaluate the limit 5(y? – 1) lim y→4 8y2(y – 1)°

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Q: Find the limit. If the limit does not exist, explain why. Vx-/2y lim (x,y)→(4,2) x-2y

A: Factories the denominator term and cancel out the common from numerator.

Q: Explain with computation and using graphs why the following limit: (x - 2)(y - 1) (2.1) - 2)2 +…

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Q: Find the limit . Xy lim (x,y) →(4,3)x² + y² 12 125 ○ 25 이 12 b 5

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Q: Evaluate the limit lim Va? + 3x + 11 – x -

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Q: Find the limit. lim (x, y) (9, 4) X + 3y – 4x - 12 y 4 %3D У -4 6. 0. O 12

A: A detailed solution is given below.

Q: (a) lim (3x + 5) = 2, I-1

A: a limx→-13x+5=2using ∈-S definitionWe need to prove that :Given any ∈, we can find S , so that…

Q: Use the properties of limits to help decide whether the limit exists. If the limit exists, find its…

A: Use limit property to solve

Q: Which of the following statements are correct for lim (,1)→(0,0) 2y +3 1) Approaching along the line…

A: If the limit from both the paths are not equal then the limit does not exist.

Q: Find the indicated limit by using the limits 6f(x, y) lim (x,y) → (a, b) g(x, y) lim (x,y) → (a, b)…

A: Given: lim(x,y)→(a,b)f(x,y)=3lim(x,y)→(a,b)g(x,y)=-5To find:lim(x,y)→(a,b)6f(x,y)g(x,y)

Q: OUse the e, & definition of the limit to prove that: lim -4x + 5 = -3 x- 2 der: lim f(x) = L means:…

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Q: Use formulas (3)–(5) to evaluate the limit.

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Q: Evaluate the limit 6 (y? – 1) lim y→3 8y2(y – 1)° 3

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Q: Find the indicated limit by using the limits 3f(x, y) lim (x,y) → (a, b) g(x, y) lim (x, y) → (a, b)…

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Q: Find the limit lim,-2- f(x) for y = f(x) pictured below. yA 5+ 1+ + 土 + -5 4 4 %3D -1+ -2+ -3+ -4+…

A: This is a limit problem

Q: Calculate the limits given below, if not, explain why. y? a), lim (xy)-(00) x² +y² b), lim…

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Q: Find the limit: lim,o (2, +h)-S(G,) if . 2 if f(2) = 23-1 %3D O (A) O (B) O (C) O (D) -7 3z+2' -…

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Q: Evaluate the limit: lim 4у — 3 %3D y→ - 2

A: Consider the given expression is, limy→-24y-3

Q: Calculate the limits given below, if not, explain why. y? a), lim (x,y)-(00) x²+y² b) lim (x)-(1,1)…

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Q: The limit lim (x,y)→(-1,2) (x²y − 3xy²) = −8 - Select one: True False

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Q: V4+h-2 lim h→0

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Q: Determine whether the limit exists. If so, find its value. If the limit does not exist, indicate…

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Q: x²y? 2.2 3. Find the limit lim (x,y)→(0,0) x4 + y4' if it exists, or show that the limit does not…

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Q: Compute the limit below. Justify your answer. 11 11 x+9 5 lim x+4 x+ -4

A: We have to find the limit:   limx→-411x+9-115x+4             00   form