The limit: x - y lim (x,y)→(0,0) x² + y² exists, and equal to 0 Select one: O True O False

Q: 3x2 + 1?y? + 3y? + 3z2 3 Show that lim (1,y,2)+(0,0,0) 1² + y? + z²

A: The given rational function is 3x2+x2y2+3y2+3z2x2+y2+z2. Evaluate the limit along the line y=0,z=0.…

Q: Use (8) definition to show that lim 2-0 Z 0.

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Q: Find the constant a such that Va ax +4-2 lim

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Q: Find the limit L. L = √x-7-1 lim X→8 X-8

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Q: Evaluate lim h→0 1 2 3(x+h) ² h 1 3x²

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Q: x 5* lim Find the limit: X+0 5 – 1

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Q: xy Let f(x, y) : and let L = lim(2,y)>(0,0) f(x, y). Which of the 8x2 + 9y2 following statements is…

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Q: Find the limits lim 1 as 2 – 4 а. х— 2+ b. х— 2 с. х— -2+ d. x→-2

A: Given, lim1x2-4 (a) x→2+→2+h, h→0 limh→01h2+4+4h-4 limh→01h(h+4)→∞ (b) x→2-→2-h limh→01h2+4-4h-4→∞

Q: Find the limits : x'+y° lim (x,y)→(1,-1) x +y

A: We have to find the limit: lim(x, y)→(1, -1) x3+y3x+y

Q: Evaluate lim (x,y) →(0,0) x³ +35x² + 7y²2 5x² + y² 11

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Q: Find the limits of the Function 2 (x + h)² – x² lim h→0 h

A: We can solve this using the L'Hospital rule. And also from expanding equation we can solve easily.

Q: Evaluate lim (tan-(t),e-2t,m²). t-1

A: We want to find given integral.

Q: Use a u substitution to find Vx – 7 – 2 lim | x-15 x – 15

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Q: Find the limits of the following functions: a) lim 2x + |x – 3| x→3 Vx2+9–5 b) lim x→-4 x+4

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Q: Evaluate lim h→0 1 2 5 (x+h) ² 2h 1 5x²

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Q: x if x < 0 F(x)=sin(x) if 0 < x≤ 3 1 if 2 < x lim_ f(x) =? lim f(x) =? lim f(x) =? x-1- lim f(x) =?…

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Q: Find the one-sided limit V4 - y? lim y -2+ y + 2

A: Given: To find

Q: Find the limit, if it exists: 3x2 + 4y lim (xy)-(0,0) x2 + y²

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Q: Part. b. True or False: lim x →∞ 2x 3e +5e 2x e -e -X = 3.

A: We will use concept of limit.

Q: Part. j. True or False: lim x →∞ 66 2 (x-3)² 3.

A: Given that     limx--&gt;∞ (66/(x-3)2) = 3 Here we have to check whether this statement is true or…

Q: Evaluate the following statement: the function 22 +y2 ye 1. 3 does not have a finite limit at the…

A: Given Function: ye-1x2+y2+xx2+y213 When moving from (0,0) to along y-axis then x=0.

Q: – 4x + 8 if x 2 Find lim f(x) , if it exists. I2 O-5 O DNE 05

A: Function given is -        f(x)=-4x+8if x≤2-5x+5if x&gt;2 We need to find limx→2f(x) if ity exists.…