1) lim-sinxr x-0

Q: . lim, 1 -2 Inx x-1

A: To evaluate the given 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: (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(2x) lim x→0 х-0 1 — сos(6х) 7* – 6* – 1 lim x→1 х2 — 1

A:

Q: Determine the limit: 12 x+ 1 tan(2 x) lim 3 sin(3 x) X- 0

A: Given limit: limx→012x+1tan2x3sin3x

Q: 1+x V1-x sin-1(x) [3] limx-0

A: To evaluate: lim[x→01+x-1-xsin-1(x)] Solution: lim[x→01+x-1-xsin-1(x)] On simplifying further we…

Q: 1 2. lim cOs X -

A: The given function rewrite as

Q: (1 cosr)dt 1. limx-0 2x -?

A:

Q: 7 arctan(x) Calculate lim 0 x3 + 6x

A:

Q: lim sin (-2 T x) = x → -3

A:

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

A: a ) given limit is as below:

Q: Q3) Find: (1) lim, 1+cos 2x (2) limx→-2- (x + 2) |4-x²| 2-x

A: Q3)1Here, we need to calculate the limit of ,limx→π21+cos2x4x-π2

Q: 1-cos 2x lim x→0 x2

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

Q: 1) lim (1--)*

A: As per our guidelines we can solve only 1 question. The rest can be reposted.    In question  no 1…

Q: 2 1 lim х->1| х — 1 X→1 X - 1

A:

Q: find: a) Lim x4-1 x2 b). Lim 10x-3 SinX

A: We have to find the following limit      alimx→1x4-1x2-1       blimx→010x-3sinxx

Q: F ind @ Dlim Ix16/ lim 1-cos 3x 9. 4-X lim (1-secx) lim CosO 9= (9 -) 2.

A: Note :- there is an error in part (a) in this part value of limit is wrong. So i am solving…

Q: 2 2- limx-1 sin(x3-1) x-1

A:

Q: 1-coskx 2. lim = 0. kx

A: We have to find the limit of the function (1-coskx)/kx when x tends to 0 .

Q: b- lim [In(cos(x))]= x->0

A: Given that:limx→0[ln(cosx)]x

Q: x- cosX X- COS X 4. lim,

A: Our Aim is to evaluate the limits given below:-limx→∞x-cos (x)x-(i)

Q: lim In (x°) x2

A: We have to evaluate the given limit.

Q: 4 Find lim х — 4 Væ – 2 x→4

A:

Q: 3. Evaluate: lim -) X-0 sinx

A:

Q: 1-cos 2x lim x2 sec x-tan x X→0 lim TT X→- 2 2

A: "Since you have asked multiple questions, we will solve the first two questions for you. If you want…

Q: ® Find Lim X->2 x¥ _ 2x² - 8 x² - 4 (2 ,X +2 Lim 3X X→3 X- 3 -3 X+3 O Lim © Lim t- fo -) ,X EO X+2 2

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

Q: х2—1 lim х-1+ In(x)

A:

Q: b) lim sin(x² – 4) х* -16 2х - 3 а) lim %3D V3x² +16 x->2 X->-0

A:

Q: 3* –1 lim V1+x -1,

A:

Q: (1) lim,o In (sec x) 3x (2) lim, (tan x)*

A:

Q: 3. Find lim x sin II

A: Given limx→∞xsin(πx)

Q: 1 lim х-0+ \x = 0 Arctan x,

A: Topic = limits  As per guidelines, At a time only one question can be answered.  please repost for…

Q: Evaluate limx=0+ e(1/x)

A:

Q: 1-cos*x 5. lim X-0 xsinx

A: Given,

Q: Find lim x→-3 sin(−4 π x)   lim x→-3 sin(−4 π x)

A:

Q: (1) lim,-0 √x+9-3 X (2) lim-0 1–c05x x sinx (3) limx-1 x²+3x-4 x-1

A:

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

A:

Q: Question 3 arctan(3x) lim ( Select) X--0 ex -1 1/x lim x--0+ In x ( Select)

A: to find:- limit.

Q: 1 lim - 1)dt x→1|1 [1 – x

A: We have to find the limit of the complex expression involving integration . first we have to find…

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

A: Given,

Q: 1. lim ux-121 X-3

A:

Q: (1 1 Calculate lim X-+ x sinx

A: Find the limit

Q: 1 lim ( - X→1 \x-1 х-1 Inx

A: Definition of limits helps to find the limit of the function. A value at which the function…

Q: 2х а) lim -1-2x (sin 2x)+² - et b) lim -4x - cos x

A:

Q: lim as x goes to 0 (sin(2x)+7x2 - 2x / x4 + 2x3 + x2)

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.