4+ sin x d. lim - 1- i cos(x+x) +2 g. lim

Q: 1+ sin x i 3. lim- 1 I+ cOs x

A:

Q: 2. f(x) = sin(x) lim sin(x) - et x + 00

A: Calculate the limit and horizontal asymptote in the following way: (2).              f(x) = e-xsinx…

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

A:

Q: Find the limit

A: We first separate the limits

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

A:

Q: cos(1/x) 5. lim (1/x)

A: Find limx→∞ cos1x1x

Q: Q1: Solve Two Only : x sin (x+sinx)" a- limx-0 sin'x b-lim0 X-xcos4x

A: Solve any two

Q: 14. lim cos x 15. lim cos(x+ sin 16. lim

A: If any function is continuous within a given interval, then its limit must exist in that interval.…

Q: 27. lim (x + cos

A:

Q: cos x lim z-n/2 sin (2x)

A: If limx→afxgx is in 00 form or ∞∞ form; then applying L Hospitals' rule we get:…

Q: x? 16. lim 0 1- cos x 1+ cos 0 18. lim 0 1- cos 0 x + x? 20. lim x- 1- 2x²

A:

Q: cos x2 - 1 2. Find lim→0 2x 81,341 123

A: Answer and explanation is given below

Q: 22. lim cos2 (x - tan x) cos 2x - 1 sin x 24. lim

A:

Q: の lim 3x? メ→ 1-cos (x) b) lim 6) Xうo

A:

Q: lim cos x→1 х — 1

A: Given, limx→1cos x2-1x-1

Q: 4. lim -0 A. -2/2 B. 1 C. 2 h D. Does not exist sin

A:

Q: sin(2Tx) lim x → 6 x² – 36 -0.3333 T O 0.1667 ↑ O -0.1667 T O 0.3333 T

A:

Q: sin(cos x) limx-n/2

A:

Q: cos(x) lim 2

A:

Q: lim (-4 0 sin x x

A: Let ,I=limx→ 01sinx-1xTaking cross multilplicationI=limx→ 0x-sinxxsinxI=0-sin(0)0sin(0)I=00Which is…

Q: sin(9x) (d) lim x – 7 (e) lim 7| (f) lim x8, COS

A: We have to evaluate the following limits

Q: 1 2 COS X = ? Lim x→0 cosh x

A: Use the properties of exponential and logarithmic functions a=elna and lnam=mlna, to simplify the…

Q: Find the limit.

A:

Q: 2x tan x+ cos I COS T lim

A:

Q: sin(4z) 7. lim I-0

A:

Q: sin (x? - 4) 1- V 1- lim 2- lim x1 1-x x2 x - 2

A:

Q: V3r-1 7. lim X- sin? x-cos(2x)

A:

Q: Q1: lim,-1 x(1 – cos-)

A: The objective is to find the value for limx→1x1-cos1x Since the given function is continuous…

Q: (x-sin x) A- Find lim,-0 1-cos X/

A:

Q: 3x2 lim x→0 cos(2x) – 1

A:

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: -2x – 1 Find lim X+0 sin 3 sin()

A: Using formulae of limits

Q: Q3/ lim Evaluate 2 (1+ cosx) ) sec x

A:

Q: 4 lim sin(x) х>0 х 41

A: Given that

Q: 2x tan -1 I + COS (b) lim

A:

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

A:

Q: 2 cosh 2, 2 0. Then the lim f(x)

A: Given function is fx=2coshx , x<0sinhx  , x≥0

Q: x sin æ+tan² I lim, 0 1-cos

A: We can solve this as follows:

Q: 1-sin /r'y| If the inequality * (0,0) 24

A:

Q: sin x - C cos 2 29. lim * - sin æ

A: We use l Hospital's Rule

Q: lim =cos メ→! X-1

A:

Q: x2 h) lim - x+0 1- cos?2 x tan 7x i) lim X-0 sin 3x sin(x? + 3x + 2) ji) lim x+ 2

A:

Q: ´1-cos x 1-cos³ 11. lim sin? x

A: The given data is limx→01-cos3xsin2x Here we use L-Hospital's rule and the L-Hospital's Rule states…

Q: x2/3 +x-1 lim x-00 x2/3 + cos? x

A: It is limit problem in which we can find the answer by applying given limit in the function.

Q: lim cos xx x-0

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.