x + y – 2 Evaluate lim (r,y)→(1,1) x² + y² + 2xy – 4

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: Find the indicated limit by using the limits

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Q: lim (4x – 3y)= -11 Prove that (r.,v(-2,1)"

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Q: z+ iz lim z+0 z+ iz equals .a None .b -i .C 1- .d i .e 1

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Q: .2 - (a) lim x + y (2,y)-(1,1) xy y+4 (b) y # -4, x 4 x lim (7.y)-(2,-4) x2y - xy+4x2- 4.x' 1 a+y-4…

A: To calculate limits by arranging fractions:(a) lim(x,y)→(1,1) x2-y2x-y=lim(x,y)→(1,1)…

Q: lim (x,y)→(0,0) (x² + x²) (х, у) ->(0,0) а. 0 b. 1 с. 1/2 d. Does not exist

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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: Find lim [x +i(2x + y)] z→1-i iz3 – 1 lim z→i z+i

A: a) Given that, limz→1-ix+i2x+y It can be written as, limx+iy→1-ix+i2x+y

Q: (1+4)* r+y xy (a) lim(æ,y)-(+0∞,+0) x2 + y? =? (b) lim(r,y)-(+o0,3) ||

A: Given: a) lim(x,y)→(∞,∞)xyx2+y2x2 b) lim(x,y)→(∞,3)1+1xx2x+y

Q: x² - 7x y +12y Evaluate lim(x,y)→(3,1) х- Зу

A: The given expression is limx,y→3,1x2-7xy+12y2x-3y

Q: 2 i (z-i) lim z→i z2+1 1 O 2i 1 -1

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Q: lim (x.y) (0,0) r + yt

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Q: lim (x,y)-(0,0) x²+y6

A: Evaluate: limx,y→0,0xy3x2+y6

Q: z² + iz lim z3 + 1 z- ob ||

A: We are given : limz→∞z2+izz3+1=limz→∞z2+izz3z3+1z3=limz→∞1z+i1z21+1z3=0+i(0)1+0=0…

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: ขน lim (x,y) → (0,0) x² +10y²

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

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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: 6 lim | 3 x² – 32 X+3 X - Enter I for oo, -I for -00, and DNE if the limit does not exist. Limit =

A: We shall find left hand limit first if it doesn't exist then limit not exist, if exist and finite…

Q: x*-4y2 Find lim (x,y)¬(0,0) x2+2y2 if it exists, or show that the limit does not exist.

A: The given limit limx,y→0,0x2-4y2x2+2y2

Q: 2 i (z-i) lim Z. z²+1 1 O 2i 1 - 1

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

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

Q: lim (VI+z- VF),

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Q: x4 - y4 25. lim (x,y)→(0,0) x ² + y2

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Q: find

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Q: In Exercises 9-14, evaluate the limit or state that it does not exist.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: (x-y)2 Show that lim does not exist. (x,y)→(0,0) x²+y2

A: We have to find the limit.

Q: x tan (x²) The limit lim (x,y)→(0,0) x2 + y4

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Q: secy-1 Lim sec2y-1 a) as y → 0 b) as y → T/2

A: To determine the value of the limit limy→0secy-1sec2y-1, apply L'Hopital's rule.…

Q: EXAMPLES. Observe that iz +3 lim z→-1 z +1 z +1 =D0 since lim %3D z→-1 iz + 3

A: Now, limz→-1z+1iz+3=-1+1i(1)+3                 =0-1+3                 =0…

Q: 1 d) limy-→0- e) lim,o (1+ r/n)" 1 f) lim→0 x +

A: L'Hospital Rule : If limx→af(x)g(x) is in the form 00 or ∞∞, then limx→af(x)g(x) = limx→af'(x)g'(x)

Q: x² + y² lim (x, y)→(0,0) V – 1 x² + y² + 1

A: Given: Let L=limx, y→0, 0 x2+y2x2+y2+1-1 To Find: To evaluate the given limit.

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: 2 i (z-i) lim z →i z²+1 1 2i -1 | 1

A: Fourth option is correct.

Q: x - y 1. lim (x,y)¬(3,3) 1 2. lim x-0 xVx + 1

A: (1)  lim(x,y)→(3,3)x-yx-y=lim(x,y)→(3,3)x-yx-y×x+yx+y (We rationalize the denominator)…

Q: y² (z,1) »(1,0) z² + y² – 2z + 1 lim =? O A. 1/2 O B. Does not exist. OC.1 D. 0

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Q: lim (x,y)→(0,0) (3 + (x² + y²) In(x² + y´

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Q: iz iz°+ 1 C - lim z -i z2 + 1

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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: lim (1,4) (0,0) x2 + y2 Prove that

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Q: 1 х — 1 x +1 h 4 (a) Lim (b) Ļim h→0 V5h + 4 – = -2 x→0 2 5 t3 – 1 = 3. - (c) Lim t→1 t-1 || +

A: Reduce the equations by rationalization or by algebraic identities to put the limits and get the…

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

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Q: lim (z,y)→(0,0) (2+(x² +y²) In(x² + y²))

A: We have to find the limit of: lim(x,y)→(0,0) 2+(x2+y2)ln(x2+y2)

Q: x³ – x+y-x²y Evaluate the limit lim (x,y)→(0,0) X-y ->

A: Evaluate the limit:

Q: x²y²z² lim (x,y,z)→(0,0,0) x² + y2 + z²

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Q: lim (x,v)→(-2,0) g(x, y) does not exist given that Show that (x+2)³y² (x + 2)6 + 3y4' 0, if (x, y) #…

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