limx¬1 x(1 – cos-) x→1

Q: lim (cos(9x)) (+) +0+x

A:

Q: lim (cos x)x² 1/x2

A:

Q: (2) 1: limx-1 sin(x3–1) x-1

A: limx→1 (2-1x)2sin(x3-1)x-1=limx→1 (2x-1x)2sin(x3-1)x-1=limx→1 4x2-4x+1x2sin(x3-1)x-1=limx→1…

Q: 1-cos' (x) lim

A:

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

A: Here we have to evaluate the given limit .

Q: lim cos x+4e* is 5er

A:

Q: limx→0  (x^2+3) / (1−cosx)

A: given example is, limx→0x2+31-cosx

Q: xCosx-In(1+x)] х-Тапх, limx-ol limx-o[ a) х-Sinx c)

A: a ) given limit is as below:

Q: lim (cos(9x)) (+) x-0+

A:

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

A:

Q: 2x -cos(2x)- 2x - (b) lim | x2

A:

Q: 1- Cos(ux) lim x-)0

A: Given expression limx→01-cos4xx2 Recall the identity 1-cos2x=2sin2x limx→02sin22xx2

Q: 1- cos(x/6) lim II

A: Solve the limit

Q: eax lim x → 0 In(1+ bx) -ах e

A:

Q: 2 Prove that limx* cos== 4 = 0. %3D - x→0

A:

Q: lim In(x2 + y?) (x,y)-(0,0)

A:

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) limx¬(1/2)-(tan x)cos x

A: Given that  1)limx→(π2)-(tanx)cosx 2)limx→0x-3(tan-1x-x)

Q: Evaluate: lim   (1−cos−1x)csch(1−x) x→1−

A: We have to find the limit.

Q: 2y-n у-п lim п cos y y-

A:

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

A: Limits

Q: lim * In(sec(2x)) x→0 (sin(3x))³

A: To find the limit.

Q: 4. Evaluate lim (cos x)¹/x². x-0

A:

Q: 5. Evaluate: lim, 0 2x- x2 sin a 1 Does not exist 2.

A: lim (2x-x2)/sinxx→0

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: 3 lim z? sin(-

A:

Q: lim 4y° + Jy18 – 1 -00

A: Given that: limy→-∞4y9+y18-1

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

A: Topic:- limits

Q: (2-4)² limx-1 sin(x3-1) x-1

A: by using limit algebra and L' hospital rule

Q: 2. limx-co √x √x+√√x+√x

A: Here we have to find the value of  limx→∞xx+x+x

Q: 7- sin-(e*) 2 lim V1 - e2x

A:

Q: Lim -> 0 Sin3ycot5y/ycot4y

A: limy→0       sin 3y .cot 5yycot4y   =limy→0    sin3y tan4yy tan5y 00farm…

Q: lim (4x+cosx) / x ? x--->infinity

A:

Q: Lim Cos t X-2SM X2

A: limx→2cosπxx-2sinπx

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

A: limx→3-x5+ex1+ln(x)+sin(x)cos(x)=-35+e31+ln(3)+sin(3)cos(3)

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: 4xy lim Compute the (xy) (0,0)

A:

Q: 1f. lim (tanx)x x->0+

A: Given,

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

A:

Q: cos 3x – cos 2x - Evaluate limx→0 x2

A: Consider the given function, limx→0cos3x-cos2xx2 applying the limit to the function we get,…

Q: 2tan x- x lim, -1 2х -sin " x,

A:

Q: lim %3D X2 -マメ

A: The solution for the above question is as shown below.

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

A:

Q: limx--1f(x) Let f(x) = (x² – 1)/C(x| – 1)

A:

Q: Which of the following will make limx→c f(x) and f(c) equal? limx→2 : (x²+x-6) limx→–1 (x³ − 2x + 3)…

A:

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.