arctan(kx) e2x – 1 lim k=1

Q: 5. Evaluate lim sin(x)-(x² +3x– e*). 1-0

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Q: 4. lim xy (xy)-(0.0) v2-e-1

A: To evaluate limx,y→0,0xy2-exy-1 Substitute t=xy, then as x,y tends to 0,0 implies t tends to 0.…

Q: - «) lim (2 – ez x→0

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Q: arctan(kx) e2x – 1 lim \k=1

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Q: Q:Prove that: Vi+x+x² -1. Lim- 12-2 cos x + lim x->T/4 sin(x - T /4) > log, 0.005

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Q: e*(1-e*) (1+ x)[ In(1–x)] 12. lim, 0 'x0

A: Recall: If we have 00 form then we apply L'Hospital Rule.i.e, limx→a f(x)g(x)  = limx→a f'(x)g'(x)

Q: a. limr→0 cos(x) b. limx→n

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Q: X x+cos (-3x) 16) lim

A: To find the limit  limx→-∞xcos-3x

Q: x-a 1. lim arcsin · ctg(x – a) x→a a T-2arctgx 2. lim x→+∞ e1/x-1 Inx 3. lim x→0+ ctgx

A: As no particular question is asked , so I am solving first three L-Hospital's rule states that…

Q: A tank initially contains 50 lb of salt dissolved in 250 gal of water. Starting at time t = 0, water…

A: A tank initially contains 50 lb of salt dissolved in 250 gal of water. Starting at time t = 0, water…

Q: sin 2t lim t- 2t

A: To find:limt→ 0sin2t2t

Q: 1. f(x) = 3(x + 2)(x – 3)²(x + 5) %3D - looc th e graph

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 7 arctan(x) Calculate lim 0 x3 + 6x

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Q: -2x lim (e cOs x) х) x → 00

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Q: lim In(r) - 0t

A: Consider the given limit

Q: b. lim cos(x)-1 x2

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Q: lim - 1, avx + 3 – b x - 1 lim If score А. 4 D. В. 2 С. 1 E. -INI14

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Q: (a) lim sih 7x (b) lim x 0 sin 7x x - 9 (c) lim x-9 x - 3

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Q: e7x + e-7x _ 2 lim x → 0 5 x2

A: Evaluate the given limit as follows. limx→0e7x+e-7x-25x2=e70+e-70-2502=1+1-20=00 Since 00 is an…

Q: 4.x 2x 7e lim 1- e4x

A: We have to find limx→∞ e4x-7e2x1-e4x.

Q: 2 sin? x lim х-0 5x(1+сos x)

A: Let L=limx→ 02sin2x5x1+cosxlimx→ac·fx=c·limx→afxL=25limx→ 0sin2xx1+cosxPlug in the value…

Q: 1 COS X 13. lim- ズ→0 14. lim e -3x+4 15. lim 4x+7 ー-00

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Q: 1-coskx 2. lim = 0. kx

A: We have to find the limit of the function (1-coskx)/kx when x tends to 0 .

Q: 1+t-V1-t lim

A: To evaluate: limt→01+t-1-tt   if we substitute t=0, we get 00 (indeterminate form)   Consider…

Q: (t³ + 8)-dt + 8)-šdt lim

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Q: (a) lim 1-cos() 3x (b) lim xe 1/x (Hint: xe

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Q: Find lim 1+1? 1-e24 -2t -1 tant, 2 2 1-1

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Q: の3 Find lim メy <xiy)-s(0,01 x+y² along the curve y=x²

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Q: 2sin x lim -0 e - 1 lim - 5 cos x o e - x - 1 4 - 4e* lim -0 xe

A: As per our guidelines, we are allowed to answer the first question only please resubmit the other…

Q: Зx +3x+5 х +2 1-cos.x (а). lim (b). lim

A: To evaluate the limit, limx→∞3x3+3x+5x3+2, plugin the limit and obtain the indeterminate form of the…

Q: (1 – V3x lim tan- 3 + x x-00

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Q: (3) Evaluate lim -(1+sin(4))t dt

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Q: 2t – 1 Evaluate lim,, tan-1, e> - t - 1

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Q: e – e-* lim I-0 x2 + 3T

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Q: 1 4. Find limx→0+ ( ) ex-1

A: Given :          limx→0+1ex-1-1x

Q: • lim In (tanx) -Lーえ • Lim V9x* + ax 2 4x-1

A:

Q: 8. Evaluate e8x - 1 lim sin (6x)

A: See the attachment.

Q: 2. (a) lim T-cos e (b) lim. -70 In R tim (0) メーール

A:

Q: In cos 2.x 4. Find lim -0 In cos 3x

A: limx→0ln (cos 2x)ln(cos 3x)Applying L'hospital rule:= limx→0ddxln(cos 2x)ddxln(cos 3x)= limx→0…

Q: 399. [T] lim e(x - 1) x-1 x-1

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Q: cos(x) - 1+ lim 14x4 Limit %3D

A: We need to evaluate the value of the following limit limx→0cosx-1+x2214x4

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: 1. Prove using e-d definition. (d) lim (4x + 3) = 7 x→1 x2 – 9 = 6 - (e) lim x→3 x – 3

A: To prove the limit using epsilon-delta definition

Q: 2x e* –1 lim- x→0 sin (2x)

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Evaluate

A: Our Aim is to evaluate the limit given below:-limx→0tan (2x)x-(i)