z²+ 1 lim ミ→i 24-1 i O -i O 1/2

Q: lim ( + y) In (² + y?) (z.y)-(0,0)

A: We can write the above expression as following :' x2+y2lnx2+y2=(x4+x2y2)lnx2+y2x2. Now, if we put…

Q: sin(1 – t) |2 – 2t| (b) [8 marks] lim t+1-

A: this is left hand limit then limit approaches from left side

Q: Find lim "(x.y)→(0,0) (4 + (x² + y? ) In(x² + y² )) Dose not exist O 1 4

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Q: A. MCQS: I. LIMITS (2x+7x+6 3x2+5x-2. 1. lim-2 ( - 2. lim,-2 x+2 A.0 B. C.D. co A. 0 B. 4 C. 12 D.…

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Q: 22 -y2 =? lim (z,1) (0,0) +y? O A. 0 O B. 1 OC. -1 D. Does not exist Reset Selection

A: Explanation of the answer is as follows

Q: 3t – 9 - lim t→o Vt2 – 6t + 5 3t – 9 lim t→-o Vt2 – 6t + 5 || ||

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Q: lim (z,y)→(0,0) (3 + (x² + y²) In(x² + y?)) 00 does not exist O 30 1,

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Q: z? +1 lim z4-1 %3D i O -i o

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Q: 2² + e4 z lim z 0 22 – e²

A: This is a form of infinity by infinity so we have to apply Lhospital rule that is differentiate both…

Q: z²+3 lim- %3D iz Z-2 7i0 7 14 O

A: Given that limz→2 z2+3iz  We need to find the limit of the given question. The solution to the given…

Q: lim (x,y)→(0,0) In(2 + x² + y?) x² + y?

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Q: k a] lim = 0 kER %3D

A: 2(a) In this question, we prove the limit of the given sequence by using   ε-δ definition.

Q: lim (4+ (2? + y°) In(x² + y²)) (1,y)(0,0)

A: Given; lim(x,y)=(0,0)[4+(x2+y2)ln(x2+y2)]

Q: ldéntities will prove useful in achie Exercise 12. Show that E, (T: – ¤) = 0 %3D | E (*: – µ)² = E…

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Q: 2/3 Determine the length of x=| for 0<ys2. Assume that y is positive.

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Q: lim zta sec z is A B 2 D nonexistent

A: Given query is to find value of the limit.

Q: az Find for z = x'y'eV

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Q: lim,- S(x), given S(x) = {7-4x, x<1 {x +2 x21 %3D

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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: 4. ·| cotl t• dt 0. lim limitinin değeri kaçtır? n In(x + 1) a) 3 b) 1 c) O 2 d) 4 Boş bırak

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Q: 3n + 2 Calculate lim V7n? +1 n00

A: The solution is 37

Q: tan X AWO Lim メーラク メ O Lim 2, 5+s° (3) Lim J-→の y生チンチアメチタ

A: Since you have posted multiple question in this question so I have solved first three question…

Q: Evaluate lim (2+ y) sin(x). (x,y) → (1,6) 02 O O o O Does not exist

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Q: z+3 lim- %3D iz Z+2

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Q: السؤال 1 lim iz?-z z-- z2-1 i o -i O 1 0 -1 O

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Q: #1. lim t-tvt 213/2 12 +3t – 5 t→ 00 #2. lim x → - o0 x' +1 #3. lim tan1 (In x) x → 0+

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Q: Ôz Ôz If Z= tan"'(2) -= 0 show that : *-+ y ôx ôy

A: Let us consider function z=f(x,y) Where f is function of x,y. ∂z∂x represents partial derivative of…

Q: A = lim %3D i = 1

A: Given that: The equation is f(x) = x 2 e x  ,     0 ≤x≤3 .

Q: 2. lim (x,y, Z)-) (0,0,0) EYaluate ベtyナスス

A: If limit depends upon the directions then limit does not exist.

Q: 23. lim Vx2 + y² In(x² + y²) (xy)→(0,0)

A: This question is related to limit in two variables.

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: lim (2,y)+(0,0) In(2 + x² + y?) x2 + y?

A: We have to solve given limit:

Q: Prove that arctan x + arctan y = arctan(x + y) / (1 − xy),  xy ≠ 1.                   Use the…

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Q: 2. Show that lim (x,y)→(−1,0) (x + 1)² sin y (x + 1)4 + y² does not exist.

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Q: sin2z+721任22 4. lim よー2 z (2十1)

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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: iz° + 1) lim z→-i\ z² 2 +1,

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Q: 2t – 2 t2- 1, Let r(t) = - î - tan (t) ĵ+ In(2t) k. %3D (a) Determine the domain of r. (b) Compute…

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

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Q: 3z+ 4y lim (2,0) +(0,0) 2z - 5y OA- OB OCo O D. Does not exist

A: Explained below

Q: finde general Sonotion 1- y' = See'y 2X-1 %3D 2- 3-Xy=Y+2x $ in?

A: This question can be solved by applying the concept of differential equation.

Q: 5-Vx+25 limr→0

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Q: In x i) lim 1→1 x² + 2x – 3 ii) lim r(, – arctan r) iii) lim z40+ iv) lim xº

A: TO EVALUATE THE FOLLOWING LIMITS CONCEPT USED L' HOSPITAL'S RULE limx→a f(x)g(x)    if  limx→af(x) =…

Q: Show that (x + 1)² sin y lim (x,y)→(−1,0) (x+1)4 + y² does not exist.

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Q: 6zy lim zy)(0,0) z* + 3y

A: Suppose we are approching (0,0) along x-axis (y=0). Now we get lim(x,y)→(0,0)6xy3x4+3y4=limx→0…

Q: Find the limit

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Q: If f(x) = xcosx then limf(x+h)-f(x) h COSX = ? %3D %3D h-0

A: