Prove: 1 a) lim Z+2i Z-1-21 b) lim 2-0 c) lim - 1 (Im²) ² IZE does not exist (Rez) 12-1 = 0

Q: 2t2X+ -1 14x2 DAna lim X-7-1 FCx) X-フー1- (-1) 2+21-)) - 2 + 1 ext O And lim 7-1t Lim X-7-1 -1+1 -…

A: Consider the given function,

Q: a' + b' + c\!/r 9" - Vabe. Geometric mean Prove that lim 3 where a, b, and c are positive real…

A: Let Take natural logarithm on both sides.

Q: Find the indicated limit. a) V3x+5-V5 lim a) b) x*+2x3-15х2 lim х-з х3+2x2-9х-18 b)

A: As per our policy we have to do only single question.  A) 3/(2√5)  B) 12/5

Q: (5) Prove: 1 a) lim z+di Z→ 1-2i b) lim. 2-0 c) lim 730 1 (1M²)². 12₁²2² does not exist (Rez) -1-2-1…

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Q: T ) lim tan 2x2 + 1/

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Q: Let ginl=√1+an To find: (i) g'(x) cliij Domain of g(x) Domain of gix. Q using definition @ g'xl lim…

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Q: Q.1 Evaluate the limit x-3 sin2x 1) lim(2x2 +x + 1) 2) lim 2-9 3) lim x-1 x-3 x2-x+1 4) lim x+00…

A: We have to find limit

Q: Prove that lim 1 H 101H 818

A: We have to prove that  limx→0- 1x → -∞.

Q: rasb then prove Lim Ja 9. that

A: If  0<a<b  then prove that limn→∞an+bnn=b

Q: Given that f(z) lim 2 2 - 1 = 3. Find (a) lim f(r) (b) lim f(x) +2- f(x) (c) lim - 2 (r2 – 1)7 (d)…

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Q: 5t3-2t2-t+1 b) t→∞ t2-2t3

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Q: Зп + 6ni ) lim n0 |2+ 3i|n

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Q: lim In(x+3) 4) 1

A: Evaluate :     limx→∞ln3xlnx+3

Q: date let fcx7= X-3x+2, find al lim fux) X-72 bllim fux) c) lim fox) (1) X-72

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Q: i) lim I-18 /976. T³ +1 Mar

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Q: d) lim √2-x X-2+ 4 e) lim (¹2) x-3x-2

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Q: x-2 j) lim -3x+2 3x+2x lim 0 x+4x k) x2 -3x+2 lim 2 x - 2x I) lim -x 1-x im m)

A: We will find the value of Given limit.

Q: True or false? if lim fcx) exists but Lim gx) does DぐX not exist, then lim. fox)+gox)) does…

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Q: 1. lim x²-1 al 2. Tく-X b) lim X-Sin 2x +3 c) lim Vey?-x

A: Given- limx→1x2-1x10-1

Q: 28)g= 5+4Eant de %3D

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Q: 4) Given that lim f(x)=3, what is the value of lim (2 f(x)-5) ? x-4 x-4 A) 3 B) It doesn't exist C)…

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Q: c) lim (x – 7) x-7 f3x + 1, x< 5 lim x-5* (2x + 5, 5<x d)

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Q: -3x + 4 a) lim x-2- x2 - 4 x2 b) lim x-3* x2 + 2x – 15 2x4 + 5x3 - 2х- 3 9x + 10 c) lim 5x7 + 2x6 –…

A: a) limx→2--3x+4x2-4=-3(2)+422-4=-6+44-4=-20=-∞limx→2--3x+4x2-4=-∞

Q: 8.) lim (-1+ x² – x³ + 3x*) 9.) x3-2x-1 lim x-3 co-X 2x2+3x+1 lim X+ 3x-5x+2 10.)

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Q: 4- Prove that lim- tan 2x 5-lim 2(-3+x)²-18) x-0 X-0 2.

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Q: + II 云 M * 00 B 2. 21 21- D N 6) lim f(x) x-1 (x)3 1. 2. -1 A) 1 B) –1 D) Does not exist 7) lim f(x)…

A: For a function, the limit at x=a exists only if : LHL(Left-hand limit) = RHL(Right-hand limit)…

Q: not exis 4) lim f(x) x-0 fex> A)-2 B) 0 C) Does not exist D) 2 5) lim f(x) X-0 f(x) 2 -2 A) 1 B) -1…

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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: a) Evaluate:- 1: lim (xcot x) I-V31 + 4 2: lim 4-1 3: lim $(x-5)

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