v3 – 8 lim 4 v→2 v* – 16

Q: 2h 4. lim h0 2h S(x) dr

A: Answer and explanation is given below

Q: arctan(kx) e2x – 1 lim \k=1

A:

Q: arctan(kx) e2x – 1 lim k=1

A: To evaluate, limx→0∑k=18arctankxe2x-1 Then, the above expression can be re-written as,…

Q: Limits involving conjugates Evaluate the following limits

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: 1 1 V 8 lim v- 8 V v→8

A:

Q: 1 1 lim v→s(vー5 ビ-25 v² - 25, 2 lim w→ -1- 1-w W-3

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Q: Find the limits

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Q: 2 9メー」 gx)= fox) =X üs I31 3メ-1 lim (fog) x メーラ

A: We have to find limit

Q: lim yn2 +n -n=0

A: Limit problem......

Q: lim 1. m, n > 1 is

A: We try to find the limit by substitution

Q: 2cosh (z) – z- z2 lim 24 12 1 3 1 12

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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: lim 17) P - (5, 5, 1) In (z\x2 + y²)

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

A:

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

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

Q: .2.4 lim (z,y)→(0,0) x² + y?

A: follow next step

Q: 8 d. lim 1+16 I-4 I- 16 V9r2 + 4 lim e. 2r +1

A: Explanation of the answer is as follows

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

A: The solution is 37

Q: Along the path x = ey find lim (1,y)→(1,0) y²-6zy 3r-y-3 does not exist O 3 0 2 0 -3 O 2 0

A: Find limitx,y→1,0lim y2-6xy3x-y-3calculate limit along the curve x=eyconcept:- convert limit in one…

Q: eim 2メー5 メ4 -2 z lim Vx+4-1-x-2 メ→ メ+3 lim 2-X Z-メ 24メ

A: You have posted multiple questions. As per the instruction, we will be answering only the first…

Q: 1. lim Vx? – 4 x→2+ – 4 2. lim /x(5 — х) x-5 4x 3. lim x-4+Vx-4 E.2

A: We have to find

Q: 1. lim (1+ Vw)(2 – w² + 3w*) 12 – 1 - 1 2. lim t-1 12 + 4t + 3 3 2z - 2 3. lim 2+2 - 4

A: we have to evaluate the limits. (1) limw→1(1+w3)(2-w2+3w3)(2)  limt→-1t2-1t2+4t+3(3)…

Q: ху — 2х — у +2 lim (K. y)-(1,2) X* + y² – 2x – 4y + 5

A: Let  S  be an open set containing  (x0,y0) , and let  f  be a function of two variables defined on…

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

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Q: lim, (V+x+1 - V+1) – Vx² x* + 1

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Q: 16-2 Evaluate: lim +4 V12+-a dne O 2 12 3 14

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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: 1 1 t 3– 5/t2+81 4 lim 3 2/t2+Vt2-16 Z X→-00

A: The given expression of limit is:…

Q: 12 -9 V5r2 – 21 (а) lim I+3 1 + 2x – 15 (b) lim 10-т

A: We need to find following limits which can be calculated by simplifying the expressions and then…

Q: Find: lim→1+i z2 –z+1-i i z2-2z+2

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

A:

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

A: Here given that three limit problem and we find its value and prove that. All limit make 0/0 form…

Q: (b) lim→0 ē2a +1

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Q: x*-16y* lim 14. (r,y)→ (0,0) x2 +4y2 xy 15. lim (x,y) (0,0) 3x² +2y2

A:

Q: 22) Find lim -5 e-2x+6 .given e =2.7 and e0 = 1. = %3D X 3 A) -13. 5 В) - 2.7 C) 0. 0 D) -5.0

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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: ー4 1. lim もラー2 t+t+ 1 to

A: limt→-2t2-4t2+5t+1 Plug x =-2 in it (-2)2-4(-2)2+5(-2)+1 Simplifying we get 0/5 = 0

Q: lim (2 + (x + y²) In(x² + y³)) y)→(0,0)

A: Here, lim(x,y)→(0,0)2+x2+y2lnx2+y2

Q: x+ 3 20. lim x-3 x + 4x +3 x²-7x + 10 22. lim x2 x-2 ? + 3t + 2 24. lim 7-1-2 Sy + 8y2 26. lim y0 3y…

A: Note: according to our guidelines we can answer only first question because there are multiple…

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: Find the limit

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Q: 6.lim 2+x-VZ

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Q: 1 (iii) lim I-bt 6 – x

A:

Q: Answer 21-24

A: As per guidelines we have to solve 21