2 cos(4x) – 4x2 – 2 lim - I→0 sin(2x)- x2 - 2x

Q: 1 + x + sin x 47. lim 3 cos x 49. lim Vx + 4 cos (x + T)

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Q: [xus (2) x+10) xuIsx(p) x(1) (k)1 ×sinx (1x [x][a] (k) 1 x (m)xcosx

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Q: 7x cos х -7x - lim [sin(-2x)sin(5x)sin(7x)] 2x3cos(x) lim 5x2 х>0

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Q: 1 - cos(3x) lim 3x х> 0 1 + Зх — е e

A: We , have                Given      lim 1-cos3x1+3x-e3x     x70We have to evaluate the…

Q: 2 lim In (cos x)e

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

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Q: In (**) 1+v1-x²' sech-1 x (A) O sech x

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Q: 2x - 6x 34. lim x-0 sin 2x 35. lim 2 1- cos 2

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Q: -Vx+ 1+ In(x) e* lim + sin (x)cos(x)

A: Find the limit

Q: cos 2x–1 lim COS х— 1 cos x-1

A: limx→0cos 2x-1cosx-1

Q: x sin 4x b. lim x-0 1-cos3x

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Q: エ→2 x² -4 1- cos 2x 7) lim X sin x エ→0

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: i) lim cos x-0 7 πCOS²x x²

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Q: T-cosx 2. limx-0 3.limx-0 sinx x2 +1 4.limx-0 x+cosx

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

Q: Evaluate f x² cos 4x dx Evaluateſ sin* 3x cos3 3x dx Evaluate the integral J x²+x-1 dx x(x²-1)

A: Given:   i) ∫x2cos 4x dx      integrate by parts ∫fg'=fg-∫f'g     here f=x2,f'=2x , g'=cos…

Q: 2 In cosy y4 1 [1] limy-0

A: After simplifying the function the form is 0 by 0. So, apply L'Hopital's rule to find the limit.

Q: Verify the identity.

A: Given: arctanx=12arctan2x1-x2. The interval given is -1<x<1. From the given interval, let…

Q: 3 cos(x) sin(4x) 3. lim x→0 2x

A: Solution:

Q: sin°(,² – 4) (x+2) tan(x+ 2 limy→-2

A: We have to solve

Q: Use Fourier cosine transform to solve y" – y = 3e-4 y' (0) = 0 lim y (x) = 0, as x → o0

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Q: 4) lim (1 + sin 4x)¹/x x→0+

A: Given limx→x+1+sin(4x)1x

Q: (c) (d) sin 3x lim z0 tan 3r lim (In(sin 2x) - In(tanz)) +0+z

A: Here we have to solve the given limits.

Q: |- lim メ→ X-3 2. lim メ→2 (会 4 メー2 メ*-4 3. lim メ→。 3メ - S;u4X 4. lim メ→。 tau3X 5- lim 1- Cose Sin'e

A: Since you have asked multiple questions. So, we are solving first few for you. If you want any…

Q: 1-cos 2x sin² x limx-0

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: 2y-n у-п lim п cos y y-

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Q: Vx 6. lim x00 In(x1000) 7. lim 3*-2x X0 x2-x 8. lim 35 sin (nx) cos2 (Tx) 9. lim X-5 2n2(x-5)2

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Q: x cos (3x – 7) cos(2x+ 7) lim cos(플-x)

A: Limits

Q: lim (x approaches 0) of [sin(5x)cos(6x)]/(x)

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Q: In(x) limx→0* 0 e = 0 cos(re-x)+2

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Q: 4 points lim h→0 2h cos(x² + 1)dx O 1 O cos(1) O sin(1)

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Q: 3. Prove that -2/3 dx diverges by showing that х lim -2/3 dx = 00 х

A: Given limit is Since one of the limit of integration is infinite , so we evaluate the limit as…

Q: 6xsec 3x 2-If y = (tan3x)²² prove that = (tan3x)²= + 2ln(tan3x) %3D dx tan3x

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Q: 2 sin (4x) lim 2. x2 (1+ cos x)

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: 3x2 lim x→0 cos(2x) – 1

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Q: sin5x(1-2t)dt (6) lim

A: limx→0∫xsin5x1-2tdtx Let  I=∫xsin5x1-2tdt=t-t2xsin5x=sin5x-sin25x-x+x2

Q: 2 cos (n²+ 3n – 7) - b, Find lim b, V3n² – 4 -

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Q: find the limit as x approaches 0. 12sin(3x)/1-cos(3x) = as x approaches 0

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Q: X+ 0.4Inx 04. limx→+o X+ 3lnx 05. lim, „(e* – 1)cosx e' – 1)cos> COSX 'x→0

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Q: lim as x approaches 0   x sin(x)/1-cos(x)

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Q: 2x + Vx x² + 4x 3 1. lim 2. lim 7x2 + 2 sin x 3. lim x→-o x + e* 4. lim et 2xe2x In x 6. lim 5. lim…

A: To decide whether the given limit produces an indeterminate form6. limx→∞lnxx

Q: 1.) lim 2x sin'x. *P0 ex - x - 1

A: We apply l- hospital rules and solve it. Follow 2nd step.

Q: sec2x-2taпх lim X→T/4 1+cos4x

A: Consider the given limit limx→π4sec2x-2tan x1+cos4x   limx→π4sec2x-2tan x1+cos4x=00 Which is…

Q: 1 lim, (e** - 1)sin-+9cos x . x0

A: Given: limx→0ex2-1sin1x+9cosx we know that  limx→0ex2-1=0 and  limx→0sin1x=-1 to 1 so,…

Q: lim COS X tanx メー→o <-2メ4リX-8 2lim 3 メ→ 2 xリ_2X メ-2 xツ_2Xメ

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Q: in(cos(x)) 2 limy→0

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Q: In x 6- find lim + 3 + /3x dx 2 Jx 7- find 4 x, +x?)– Inx² -e In 99 dx | In(x 8- find (x+1) In°…

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Q: 2x +5x-3 1. lim 6x -7x + 2 4x-6x+3 lim 16x +8x-7 4. x'+8 7. lim 2x-16 1 -1) h-0 hV1+h 10. lim ) sin…

A: 1) Here, the direct substitution  of the limit value will lead the denominator of the function to be…

Q: 1. lim 3r+2r+1 X-n Sx2+7x+4 2. lim +sinx

A: See 2nd step