et – 12x + I lim r4 +1 e* +1 lim 1H00 I - 2 lim sin

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

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Q: (2-4)* Q1: limx-1 sin(x³–1) x-1

A:

Q: 1 (a) lim 2x+sin x 5x+2 (b) lim 1 (c) lim cos -

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

Q: 9. Lim 6x - Sin 2x メ→0 2x +3sin 4X b. lim x²-1 1/2

A:

Q: a. limr→0 cos(x) b. limx→n

A:

Q: 5. x sin 3) lim00 x+1

A: limx→∞x5sin5xx4+1=limx→∞ x5sin5xx41+1x4= limx→∞ x sin5x1+1x4 = limx→∞  sin5x1x1+1x4=limx→∞ 5…

Q: (12 sin )( In x) (x3+5)(x-1) Evaluate limx→1

A: Here we have to evaluate the given limit .

Q: 1-sin t lim 1+cos 2t t- 2

A:

Q: 1 2. lim cOs X -

A: The given function rewrite as

Q: sin 2t lim t- 2t

A: To find:limt→ 0sin2t2t

Q: sin(1 – t) |2 – 2t| (b) [8 marks] lim t+1-

A: this is left hand limit then limit approaches from left side

Q: Show necessary computation x²-9y? lim (x,y)→(1,0) tan-1 (x4 – 4xy + y²) lim (х,у)-(0,0) х-Зу b. а.…

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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: 1- cos(x/6) lim II

A: Solve the limit

Q: 1) limy-o 2ytan(1/y) sin(r-0²) 2) lim2n 101-Va 2 3) limg-n/2 (n²-482 )sec\ß] tan2x 4) lim T

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

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Q: 44. lim sin² x x→n/4

A:

Q: 16 |how do you express limn→0 0 Li=1 - (5+ £)9/ as п definite integral

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Q: i) lim(In (3x– 2)– In(5x+4)) Зх +1 lim 1 j) x0* sin x k) lim (csc x- cot x + cos x)

A:

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 a sin(1/2),

A: Given,           limx→0xsin1x

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: 6.The lim x +3 is equal to 1S 3x-4x+n sin t. 7.The [1 is equal to

A: As per guidelines we can answer only one question at a time so if you need more answers kindly…

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 + sin 2x lim x-2 x – sin 2x О з O 2 O 1/3 О 12 O other:

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: 3. Find lim x sin II

A: Given limx→∞xsin(πx)

Q: #1. lim t-tvt 213/2 12 +3t – 5 t→ 00 #2. lim x → - o0 x' +1 #3. lim tan1 (In x) x → 0+

A:

Q: Q2: Evaluate: [1] 21 lim m COSXVI+ COSX – v1-x, sin-1(x) V1+x - [3] lim-o

A: Limit of a function determines the continuity of a function. Three types of limits exist, one is…

Q: Rewrite the following as one-sided limits as in Exercise 50 and evaluate.

A: To evaluate the limit. (a).…

Q: 1 1 X sin x+sin 2x Q3/ Find the value of (x) if5 -2 1= lim 3x -1 1

A: See the attachment

Q: (2-4* limx-1 sin(x³–1) X. x-1

A:

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

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

Q: (x+h)³-x³ lim h→0 h. sin(3w) lim w-0 2w sin(h)(1-cos(h)) lim

A: We know (a+b)3 = a3 + 3a2b + 3ab2 + b3 limx→0sin xx = 1 limx→01 - cos xx = 0

Q: 1– tan(*,) [1– sin x] lim 1+ tan(x (¥2) [z – 2x] x- - 2 1/8 1/32

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

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Q: AWO Lim tanx L Szx Lim X-CSc メーラク メ メラ。 OLim ()) S→の 6 Lim di6-X +1XI メー→ロ y4 (3) Lim J→ y2ラッチアy49 4…

A: 1. limx→0tan xx2. limS→∞SS+1S25+S23. limy→∞y4y4-7y3+7y2+9 Note:    Multiple parts are given, we are…

Q: 2. Evaluate cosxsin2x lim 1 – sinx

A: We need to find limx→π2cos x sin 2x1-sin x Now, put the limit in the function, that is put x=π2 .…

Q: ut. AW O Lim tanx Lim X: CSc Jzx メラ。 メーラク のLim 5→の 6 Lim 16-X + 1x1 メーラマ Sinx 3 Lim 3-→ yテンネマ4 のLm(…

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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: 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

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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: х(4+sin 6x) 3. lim X→+0 х+1

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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: not exist". x2 + 3x + 2 (а) lim x-2 x +2 cos O 1 (b) lim 0→0 sin 0 (c) lim In(sin r)

A: To evaluate the following limits: a limx→-2x2+3x+2x+2 blimθ→01-cosθsinθ climx→π+In sinx

Q: Q2) Find : (a) lim (2 + x) x-4+ 16-x 1-secx 0 sinx cos2x sintx (b) lim (c) lim (d) lim x-0 sin2x…

A: Dear student, According to bartleby guidelines when student post more than one question then expert…

Q: If f(x) = xcosx then limf(x+h)-f(x) h COSX = ? %3D %3D h-0

A:

Angles

In mathematics, angles constitute a very important part. Just like the concept of lines, an angle is a necessary figure that is used for measurement. How do you define its formation? It is formed when two or more lines meet at a point. The point at which two or more lines meet is known as the vertex. When the lines get inclined at this point, they do form various angles. Angles are measured from the vertex in terms of degrees.