x? - 2y2 lim (x,y)-(0,0) x2 + 2y2

Q: x²-2xy+5y²+1 lim (x,y)→(0,0) 3x²+4y²+2

A:

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: + xy² + y³ x2 + 7y² 2x3 b) lim (x,y)→(0,0)

A:

Q: 2x4 y lim (x,y)→(0,0) x³ + 6y²

A: We will discuss about the given limit.

Q: X-3 lim y→3+ Vx2¬-9 х2-9

A: Find the limit of limx→3+x-3x2-9

Q: Find the limits by rewriting the fractions first.

A:

Q: xy3 lim (x.y)-(0,0) x* + y+

A: Here we go towards origin via two different straight ling and got two different limit so the limit…

Q: x2 – 1- y lim (x,y)→(1,0) X – Vy +1

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Q: lim (1.)(0,0) r +y – a²y²"

A:

Q: Evaluate

A: To evaluate limx→0 e2x-1xSubstituting x=0 , 00 form is obtained Hence , L' Hospital's rule can be…

Q: x²y Find the lim (x,y)→(0,0) x4+y2 '

A: Find the limit

Q: (x²y3 - 5y2) lim (x, y) →(4, 2)

A: Given that, There is an expression of limit is following, lim(x, y)→(4, 2)(x2y3-5y2) We have to find…

Q: t2+3t+2 2. lim t--1 t2-t-2

A: To find the limit of the given function

Q: a) xy + y lim (x.y)→(0,1) x² + y? b) 2a2 + Y lim (x,y)→(0,0) x² + y3 c) a*y+ xy? lim (1,y)→(0,0) x²…

A: Part a.) and c.) limit exist only part b.) limits not exist

Q: lim (x,y)-(0,0) x²+y6

A: Evaluate: limx,y→0,0xy3x2+y6

Q: x--2xy lim (x,y) - (2,1) x²-4y² .A 3 .B 1 4 .C .D 1 2 ONIM

A:

Q: F (x, y) = 2xy(x²-y²) x2+y2 1) Find lim f (x, y) when (x, y) (0,0)

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Q: Vx +1- 2 (c) lim x→3 X – 3 2e-* +3 (d) lim 3e* +2 00-X

A: Topic:- application of derivatives and calculus

Q: ขน lim (x,y) → (0,0) x² +10y²

A:

Q: + h 4 (a) Lim×-1'x+1 X (b) Lim h→0 V5h + 4 – 2 -2 - t3 – 1 3. (c) Lim t-1 t-1 II

A: To show the given limits, we use the algebraic indentity and rationalization of a fraction.

Q: x-y+7Vx - 7Vy lim Vx - Vy (x,y)→(0,0) x+y

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Q: lim xy + 2y - 3x - 6 (x, y) 4, 3) y +3 y-3 2 O 6

A:

Q: xy - Y lim(x,y)→(1,0) (x − 1)² + y²

A: Please see the below picture for detailed solution.

Q: 5x - 1 b) lim Z-+0+ 10z

A: We have to find

Q: .2 lim (x, y) (0,0) along y = x2 |3|

A: Substitute y=x2 in the function. Now the limit becomes

Q: 2r²y² – 2 (a) lim (z.y)→(1,1) x² + y² – 2 2r²y² – 2 (b) lim (z.v)(-3,4) x² + y² + 2 VI+ y – 4 (c)…

A: a) Given lim(x,y)→(1,1)2x2y2-2x2+y2-2  put  x=1+r cos θy=1+r sin θ…

Q: 2x*y? =? .4,2 lim (x,y)→(0,0) x4 + 3y4

A: We find the limit of two variable along the path.

Q: 4r3 + 6x² – 2 a. lim 0 2r3 – 4x + 5 V9rº – I b. lim 1-0 r +1

A:

Q: xy – Y lim (2,y)(1:0) x2 + y² – 2x + 1

A: We have to solve given problem:

Q: xy lim (x.y)→(4,3)x²+y²

A: find the following limit

Q: x° +2y² +x*y lim (* ,y') → (0, 0) x* +3y - x*y

A:

Q: 2x²-xy-y² x2-y? Evaluate lim (x.y)-(1,1) 3. 2 0 2. 20 2/2 2. 10

A: Answer

Q: x3-8 lim = 0 %3D х-2 х4—16 FO

A: As per our guidelines we are suppose to solve only first question. Kindly repost the other question…

Q: tan ( xy) :? lim (х.,у) -> (0,1) х-y+x 1 (e) (d) - (а) 0 (b) 2 (е) 1 4

A:

Q: x² + y? lim (x,y)→(0,0) /x² =? + y² + 1 – 1 A. -1 В. 2

A: In this question we will use basic of calculus i.e concept of limits of two variables.  To find…

Q: (d) lim Vi + 2x – V² – 2n - 2r I+ VI (e) lim 100 - z (f) lim 1 r- 2 I+1

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Q: lim х-2 x→2 Vx + 7 - 3 Score С. 1 А. 6 В. 4 С. 2 D. 0

A: As we can observe that it is an indeterminate form(0/0). To solve the limit, multiply and divide the…

Q: x*-16y* lim 14. (r,y)→ (0,0) x2 +4y2 xy 15. lim (x,y) (0,0) 3x² +2y2

A:

Q: y+4 lim (x,y )→(2,-4) xy -xy +4x-4x

A:

Q: x² yey lim(x,y)→(0,0) x4 + x + y²

A: To evaluate the following limit.limx, y→0, 0 x2yeyx4+x+y4

Q: Vx - Vy+9 lim (х,у) —(11,2) x#y+9 х — у—9

A: The limit of a function at the value of the variable is the value of the function when the value of…

Q: a) lim x-3 x+1 x2 – 4x + 4 b) lim x-2 x2 +x - 6 y? – 4y – 21 c) lim y-7 3y2 – 17y – 28 t3 +t2 – 5t +…

A: NOTE-Since you have asked multiple question, we will solve the first question for you. If youwant…

Q: x2y2 lim (r,y)(0,0) 2r+ y

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

Q: ry - y lim (z.y)(1,0) (z – 1)² + y²

A:

Q: Find the limits

A: We have to find the limit: limx, y→0, 03x2-y2+5x2+y2+2 Since it is simple determinate limit so…

Q: 2xy lim (x.y)-(0,0) x² + 2y6

A:

Q: x2-2xy lim (x,y) - (2,1) x²-4y2 .A .B 1 .C 1 .D 1 4

A: We have to evaluate the following limit. lim(x,y)→(2,1)x2-2xyx2-4y2

Q: tan(хy) = ? x²y (х, у) -> (0.1) х*у+х ¯y+x lim

A:

Q: t² +3t t--3t²-t-12 b. lim (-3)²-9 u-0 น (x+h)³-x³ C. lim h→0 h a. lim

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…