What is the value of x - y, if x and y satisfy the following? lim (2² – 52) = x + iy z-2-3i Your answer

Q: x(1+acosx)-bsınx Find the values of a and b so that lim exists and equals 1 x3

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Q: (a) Find constants m and n such that lim (xel/x – (mx + n)) = 0. %3D

A: Given,

Q: 2i Part (a) lim EI=n 2 n V n i=1 n-00

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Q: 2z-i Our aim is to prove that lim = 2. Which among the following options is true? Zco z+1

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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: (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: lim Σf (xf) Δx)]. V Axi→.

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

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Q: lim xy - 2y =? T,y)→(2,0) x2 + y? – 4x + 4

A: We have to evaluate the following limits -  lim(x,y)→(2,0) xy - 2yx2 + y2 - 4x + 4

Q: e2t - e-2 – 4t lim- t- sint

A:

Q: Given lim (0,y)→(0,0) x4 + y? 1 and lim (2,22)→(0,0) x4 + y? 2 does lim (2,y)→(0,0) z1+y? exist?…

A: We have to find whether lim ( x, y ) tends to ( 0, 0 ) x2y / ( x4 + y2 ) exist or not .

Q: Q27. The value of lim (1+x)5-e5x+sin x² is? e x2

A: The given limit,limx→01+x5-e5x+sinx2x2

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

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Q: 2x?y lim (1,9)→(0,0) x4 + y² O A. 1 =? O B. 00 O C. Do not exist. O D. 0

A: The option C is correct.

Q: 2 i (z-i) lim z?+1 1 -1 о 2i

A: 1 Just use L'Hospitals rule.

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: 3. Find the values of the constants a and b such that Va + bx – V3 - lim x → 0 3.

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

A: To find:-

Q: 2.r The lim x² using L' Hospital's Rule, is: x>0 А. 1/2 В.О С.2 D. 00

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Q: 16. lim, (1+) =c, then lim, (1 + =? A. 2e B C.eD. e В. X→8∞

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

A: .

Q: Given that lim (5x - 5) = 15, illustrate Definition 2 by finding values of d that correspond to ɛ =…

A: To Solve this problem we use here the definition of limit at a given point.

Q: f(z)' lim Z→Zo Lg(z). A В

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Q: a, = V 2n + 6" %3D lim an %3D

A: Given: an=2n+6nn The main objective is to find limn→∞an

Q: Determine the value of c for which 42 8n lim (1+ n00 cn

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Q: Sirlw)dk= f (x) κ= lim Σ fx%) Δx 25.) Use the definition, -2x n+00 i=1 to evaluate Σ Ei=" (n+1) Eř="…

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Q: x? — х -2 lim 2 x +3x + 2 X→-1 X

A: First we factories then take limit.

Q: x²+3x (t – 1)e' dt 2л — 4 - lim x→2

A: Given limit is : limx→2∫10x2+3xt-1etdt2x-4dt To find the value of limit by using L’Hospital’s.

Q: Along the path x = e y +6xy find lim (x.y)→(1,0) 3x-y-3 Along the path x = e y? +6xy ind lim…

A: Let's find.

Q: e – e-* lim I-0 x2 + 3T

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Q: Use the L' Hospital Rule to find : lim In ( csc? x) x → 3n (2 (x -37/2)2 lim Ja'y +a-a 8h - (1…

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Q: find

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Q: tan(xy) = ? lim .2. (х.у) >(0,1) х*у+x 1 1 (b) 1 (e) (d) - (а) 0 (e) 1 4 - |3

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Q: k 2**1 ak+1 When using the Ratio test for 2 k=1 3k-1 we have lim Select one: a. 3 b. 1 C. d. 2/3

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Q: a" +b" V lim /x AND= Vab tan x fii lim Anao e 2.

A: Given: iv)limx→0ax+bx21x iii)limx→0tanxx13

Q: e? – 1 – z lim 2 z-0

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

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

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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: e-1 t+1 Vi' i +21 ' -1/ In (1 +1)* lim Evaluate

A: Distribute the limit.

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

A: We have to solve given limit:

Q: (c) lim r³/x² 3/22

A: We have to find the limit value by using L'Hospital rule.

Q: Evaluate the following limits.

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Q: If lim f (x) = 9 and lim = 1, then lim 1+ = ? %3D A) 0 B) 1 C) e? D) 2 E) Does not exist

A: Given:  limx→∞ f(x)=∞    and    limx→∞ f(x)x2…

Q: x3 lim (x,y)→(0,0) x²+ y² O A. Do not exist. =? О В. о C. 1/2 O D. 1

A: Use squeeze theorem

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: ax? + sin? Let a be a nonzero constant such that a + 27. Let f(x, y) and let L lim(z,y) >(0,0) f(x,…

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Q: tan (xy) lim = ? (x.y)→(1,0) y+xy (c) 3 (d) - (e) 1 (a) 0 (b) 114

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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: [x-al (a>o) Lim x+ 80a - la 2

A: From the given problem: limx→a-x-ax2+80a2-9a