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

Q: (#1) lim (#2) lim (x,y)(0,0) x2 + y? (1,y)(0,0) (x2 + 2y6)2

A: ggg

Q: 2xy3 lim (xy)-(0,0) x² + 2y6

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Q: Give precise definitions of the following statements.

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Q: x, x 2. y=h(x) 4 3 y-2 Show that a. lim h(x) + 4 b. lim h(x) + 3 c. lim h(x) + 2 X-2

A: Given, h(x)=x3,  x<23,  x=2  2,   x>2 now show the limit on x→2…

Q: tan (xy) lim = ? (х., у) -(1.0) у+ 2ху (b) - (e) (c) 3 (d) - 4 (a) 0 (e) 1

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Q: Va +t - Va -t lim t 0 for a > 0

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Q: fem - lim fex) &(X+h)-f(x) %3D

A: Differetiability definition .

Q: cscy+1 lim 1-secy a) as y→n/2 b) as y→t/4 с) as y> Зп/2

A: (a) Given,lim cosecy+11-secy Find the value of limit as y→π2 Hence, limy→π2…

Q: f" (h+x)-f" tx) Then lim %3D

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Q: 2x – x y- 3y² a. Evaluate lim, (x,y)→(-1,1) x+y

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Q: 3 sen y lim (xy)-(3,0)

A: Since lim(y tends to 0) sin( y)/y=1 Therefore, lim(x,y)tends to (3,0) x^3sin(y)/y=(3)^3×1=27

Q: ger lim f(x)=0 ise, lim f(x) sin- X-C = ? A) -1 B) 1 C) 0 D) 2 E) mevcut değil

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Q: Find the limits

A: The given expression is limx,y→3,4x2+y2-1

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 fi + gx7 (0ʻ0)–(h'x)

A: If a limit exists at any point then if we come to any path to that point, the limit will be the same…

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: [f(x,y)] 4- lim (x,y)→(a,b) Lg(x,y)]

A: Please see the answer in step 2

Q: tan2x 4) lim, -X, 2 x- 2

A: Explanation of the answer is as follows

Q: 3x2 1) lim (x,y)-(0,0) x2 + y² + y2 ysinx

A:

Q: lim,-«G)* + x²+4 ()* limx--o %D 3x +1 a. -1 1 c. -3 Od. 3.

A: Given, limx→-∞53x+9x2+43x+1  We have to evaluate the limit.

Q: lim Scy+1 1-secy a) as y→n/2 b) as y→T/4 c) as y→ 3t/2

A: a) y→π2 lim cosec y+11-sec y=cosec π2+11-sec π2=1+11-∞=-∞

Q: 7xy lim Find (x,y)→(0,0) Vx2 + y? if it exists. 1. 7 2.0 3. The limit does not exist. 4. 3.5 5. 14

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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: り Lar Po-S 2x45 fo) =S 2x45 XくO 3-5x 1+4X+x3 find (0) lim fox) (6) lim fa) メー→+0 X -00

A: To find the limits of the given function f(x)

Q: メ*+リ tyz Evaluate limxy)(0,0) x²+ x* +y? 十4-2

A: It's a fairly standard evaluation of the limit: Multiply the numerator and denominator with the…

Q: find

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Q: your a ;) lim x4+メーLo メ→。 i) lim 左十 \im tメーLo X→-∞ iii) \m 4a(a+)しメー2)しメ+ム) メ→ ○

A: Since you have asked multiple question, we will solve the first 3 question for you as per our guide…

Q: e? – 1 – z lim 2 z-0

A: The given problem is: limz→0ez-1-zz2

Q: tan³ 2x r3 lim x→0

A: Given that: limx→0tan32xx3

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

A: lim(x,y)→2,1x2-2xyx2-4y2

Q: tan(xy) lim (х, у) -(1,0) у + 2ху 1 (с) 3 (d) 4 (а) 0 (b) (е) 1

A:

Q: - Find lim Re(2) [Hint: use z = x + iy.] z -1- i - Find lim 2+1+i 22 – 2z + 2

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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: 2. lim 七や~1 Sx?+3-2, zー1

A: To Find the Limits of function 2.) limx→-1 x2+3 -2x2 - 1

Q: Along the path x = e y²+4.xy find lim (x,y)→(1,0)3x-y-3 Along the path x = e y² +4xy 3x-y-3 .2 find…

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Q: Solve メ<。 FCX)= [ X - , メ-o x 7o 2. Can be dis played as i FCX Js X-I when x <o,I when X-0,X-l wh en…

A: To show that the functional value at x=0 and the limit as x tends 0 are not equal.

Q: lim(z – 1) csc TZ Is

A:

Q: Calealate: C lim (y-x )(1+n)

A: The objective is to solve the limit limx,y→0,0y-x1+xy+x1+y Let, y=mx Then…

Q: ANS: (d) |z - 3| lim 243- 12 6 - ANS: -

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Q: x +y – 3 Evaluate lim (x,y)→(1,2) x2 + y? + 2xy –9 Leave your answer correct to two decimal places.…

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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: ry - y lim (z.y)(1,0) (z – 1)² + y²

A:

Q: lim (x, y) → (4, -2) x2y + xy2 x? – y2

A: The given expression of the limit is: lim(x,y)→(4,-2)x2y+xy2x2-y2

Q: x²y 3x2 A. В. lim (x,V) - (0,0) x2 + y? 2y? lim (x,) - (0,0) > ) x² +y " x³y+x²y³ C. lim D. lim…

A: we have to find limit

Q: Along the path x = e" find y +4xy lim (х.)- (1,0) Зх — у -3 does not exist O -2 -3 2 0 30

A: Explanation of the answer is as follows

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

A:

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.