x2 – lim x + sin x 2x x→0

Q: 1. sin(2x) lim X = 0 4х x° – 2x + 1 f(x) - x* + 3 Find all zeroes of f 2.

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Q: 8. (x - 1) dx √x lim

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Q: 1 lim (x² –1)sin x+1

A: To find out the limit.

Q: 2. Find if possible: sin(nx) a) lim x-4 x2-16 b) lim x (sinx+(cosx)³) (x2+1)(x-3) c) lim,--o (cosx)

A: a) Given that limx→-4sin(πx)x2-16we have to find the limit of…

Q: tan x lim 3) Vx+1-1

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Q: sin x 3. lim х-30 1 — соSX

A: L Hospital rule

Q: lim х>1 \x-1 X→1 Inx,

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Q: sin(2Tx) lim x → 5 x² – 25 O 0.2000 T O 0.4000 ī O -0.4000 T -0.2000 T

A:

Q: cos x lim X-0 x2-x+3 lim 1-vx-6 x-7 x-7 X+7

A: We have to find out limit

Q: ) lim Sin (x3x+2) メーラー x3+1

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

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Q: 1 2. Lim x0x 1 sin x

A: Given:      limx→0+1x-1sinx simplifying we get     =limx→0+sinx-xxsinx Apply L'Hospital's Rule:…

Q: x sin(3x) lim x→0 sin(x2)

A:

Q: lim xS0 cos2x - cos x / x^2

A: To find: limx→0 cos2x-cos xx2

Q: - 2 lim c. x→o Sin(x)

A: It is given that X approaching 0 from the left, X<0. Therefore, Sin(x)<0. Therefore, the…

Q: x* – 1 f. lim x-1 x In x sin 3x g. lim x-0

A: (f). Given: limx→1xx-1xlnx   As we know that; The Chain rule: fgx'=f'gx·g'x

Q: x sin(x-1) с) lim х+1 2х2-х-1

A: Solution: The objective is to find the limit value of the given function

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

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Q: x + sin x 5. lim x 2x + 5

A: We have to solve:      limx→∞x+sin x2x+5

Q: 9. lim(1+ sin²x)x X-0

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Q: 5. Evaluate lim sin(x)– (x² + 3x – e*). (x³ – 2x2 - 6 + 3x) 6. Evaluate lim X→2 х - 2

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Q: Vx+2-3 (a) lim x→7 х—7 4x +3x – 10 | (b) lim х> -2 х* +8х +12 sin xcos x (c) lim x→ 0 x(х + 6)

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Q: lim x→0 tan2x-2sinx x3

A: A detailed solution is given below.

Q: 8. lim vx +6x+1-Vx² +x

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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-x c) lim- x1 1-Vx こ 11- sin x d) lim エー→0

A:

Q: (1 – V3x lim tan- 3 + x x-00

A:

Q: 4x(1 — сos(x)) lim х — sin(x) х>0

A: Because the limit is in 0/0 form. Apply L'hopital's rule.

Q: Inx lim X+o x3 lim- x-0 ex - x2 - 1 lim- 0 sin'3x

A:

Q: xsinx lim x→0 e*+e¯x-2cosx

A: Since, we have been given up the expression:-limx→0 x sin (x)ex+e-x-2 cos (x)-(i)Since,on applying…

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: tan nx 3) lim x→0

A:

Q: 4-V16+h 9. lim x+sin x 12. lim

A: Note: As per bartleby guidelines for more than one questions asked only one question is to be…

Q: 2.r + x sin 3.x 1. lim * 5x - 2x +1

A: Here we find limit

Q: (2-4* limx-1 sin(x³–1) X. x-1

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Q: 1 Evaluate: lim (1+2 sinh x)+20 x→+∞

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Q: Q4:Evaluate 1) lim (1-1) x-0 \sin x

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Q: x+xcosx lim x-0 sinx cosx

A: We have to find the limit of (x+xcosx)/(sinxcosx) as x tends to 0

Q: x2+x a. lim X-0 sinx

A: We have to evaluate the given limita) limx→0x2+xsinx

Q: 2 sin x-sin 2x lim х-sin x 3 O -3 6 -6 о O O

A: Given- limx→02sinx-sin2xx-sinx To Find- The valuie of the limit.

Q: 8 sin((k – 1)x) sin (2x) П ¤(ekz – 1) lim \k=2

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Q: V+12-4 3 .lim X-2 tan3x 2. lim X-0 sinax 4). lim X00 x-7x+1 x-2

A:

Q: (x+3)x+2| 2- lim (x+ 2) 4- lim x+0 sin x

A:

Q: ¶/x x-0 sin (1 /x) Lim

A: To evaluate: limx→∞π/xsin(π/x)

Q: 2x (1) lim x→0 3– vx+ 9 -

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Q: 1-cos(x) lim x→0

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Q: х — 1 lim x→1+ Vx + 2

A: Here we need to find the right hand limit only.To find the required limit substitute the variable…

Q: 10 sin(4x³) 12x8 lim X→0

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…