b. Evaluate the following limits: lim 7* cos)-7x – lim 5x2 COS [sin(-2x)sin(5x)sin(7x)] 2x*cos(x)

Q: Evaluate the following limits: 1-cos¹(x) (i) lim zsin(2x) (ii) lim In (√) +1 2²-1 (iii) lim sin(x) -…

A: Given :limx→01-cos4(x)sin(2x)lim x→1 lnxx2-1lim x→π4 sinx-22cosx-22lim x→01+tan(2x)1x

Q: b. Evaluate the following limits: 7x cos)-7x lim- [sin(-2x)sin(5x)sin(7x)] lim 5x2 2x cos(x) X-0

A: We write the given limit in the following format

Q: Find the limit  x appraoaches infinity (e - 2x cos x)

A:

Q: х — 1 X - 1. lim ( 1 2x – 1 |4x² – 1| x→2

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Find the following limits if they exist. 1 lim 1 a) b) sin x-1 lim cos x

A:

Q: Which of the following limits is in an indeterminate form? Select all that apply. sin x lim х—1 х —…

A:

Q: 1. Find the limit of the following functions: lim 00x/3+ cos x 1-cosx lim X-0 sin2x

A: To find the limit of the given functions

Q: 1. Find the following limits. 2 sin(2x) – x (a) lim

A: Our Aim is to find the limit of the following expression given below:-limx→0 2 sin (2x)-xx-(i)

Q: Evaluate the limits: lim (cosx)cor*x 13. Ans: e12

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Determine the following limits analytically.

A: Given, limx→π3sinπ3-x2cosx -1

Q: 1. a. Evaluate the following limits and find the value of K from the given equation: lim( x→1 Nx5-N…

A: Here we need to find Limit by using L'hospital rule.

Q: Evaluate the following limits tan x – sin x sin(x – 2) (a) lim x→0 x(-1+ cos³ 2x) (b) lim x→2 Vx + 3…

A:

Q: We can use direct substitution in computing limits provided there is nodivision by zero, which is…

A:

Q: 4. lim ¹-cos 2x x-0 sin 2x

A:

Q: Compute the following limits if they exist. sec x – 1 (a) lim I0- x – sin a (b) lim I40 x – tan x 2…

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

Q: sin(9x) (d) lim 0

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

Q: Find the limit. За + 5 lim x→0 x – 4 O -5/4 O DNE O 3

A: Limit problem

Q: Evaluate the limit: 1-Cos(9h) lim h h >0

A: Find the limit When we plug in 0 for h, the denominator becomes 0 So it is undefined.

Q: I. Evaluate the following limits. 1 1 1. lim x – 1 et — е x→1+ - - tan x 2. lim (sin x x→0+

A:

Q: B. Evaluate only three of the following limits tan 30 lim 0-0 sin 80 x+1 i. ii. lim + zX co-x 1 = 2…

A:

Q: 14. Evaluate the following limits. (3-x+x2, 5x+1Y e) lim 2x y-0+ 5x-7 lim 2 f) X0o ( 3x2 x sin x lim…

A:

Q: Q2.) Find the limit lim X+x cos x 1. X→ 0 sin x cos x

A: We find limit x+ x cos x lim X → 0 Sn x cos x

Q: Determine the following limits analytically.

A: limx→0  3tanx - 8x3x + sin2xlimit = ?

Q: Evaluate teh following fucntions

A: Dear Students,  “Since you have asked multiple questions in a single request, we will be answering…

Q: Evaluate the following limits: cos()- lim x-0 )-7x lim [sin(-2x)sin(5x)sin(7x)] 5x2 2x°cos(x)

A:

Q: Evaluate the limit of a. 3 b. O tan 2x-2sinx as x approaches to 0. c. Undefined d. Infinity

A: As per our guidelines we are supposed to answer only one question. Kindly re-post other question as…

Q: 2. Evaluate the following limit. 1/x lim (1– sin 3x)"* x→0*

A: Given, limx→0+1-sin3x1x    We have to evaluate this limit

Q: Evaluate the limits sin3h-2h 4) lim sin?x 5) lim x 0 1-cos x

A: (4) limh→0sin3h-2hh=sin3(0)-2(0)0=00=indeterminate form Apply L'Hospital rule,…

Q: lim sin?(2 – x) cot²(x² – x – 2) - X→2

A: We have to evaluate the limit at x= 2.

Q: Q4: - Evaluate the limit of the following: x3–1 sin 2x 1-V 1) lim 2) lim x→0 2x²+x 3) lim x→1 1-x…

A: When we get 00form, we can us  L' Hospitals Rule to calculate the limits. In this rule μx→a…

Q: Q3: Find the following limits if exist:- 1-cos 2x (1) limx-0 sin² x

A: If it is required to evaluate the limit limx→af(x)g(x)=00. That is if applying the limit leads to…

Q: 1. Find the limit of the following functions: lim x + cos²x 1- cosx lim e sin2r

A:

Q: Q1: (a) Find the limit of the following: x2+3 sin x 3) lim x0 ex-1 1-cosx 1) lim 2) lim ++zx 00+x X0…

A:

Q: Evaluate the following limits: tan 0 1) lim 0-0 02 cot 30 -x* 2) lim x00 x-7 x3+7x²+1 x+3 3) lim x-3…

A: (1) The given limit is: limθ→0tanθθ2cot3θ=limθ→0sinθcosθθ2cos3θsin3θ=limθ→0sinθsin3θθ2cosθcos3θ It…

Q: sin 3x x-0 tan 4x 3. lim

A:

Q: What is the value of a if the limit of the function is 3, given by еах —1-ах lim X→0 ex2. = 3? -cos…

A:

Q: . Evaluate the following limits. 1.lim cos .2 () 2. lim sin x→0 (- 3. lim 3¬× X→-2

A: 1. limx→πcosx22. limx→0sinxx3. limx→-23-x

Q: Q1- Evaluate the limit :- 1- lim - ( - cos) (1+ sin ) ) (1 + sin±)

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

Q: B) Evaluate two of the following limits 2) lim(cos² x – sin² x) - 8

A:

Q: II. Evaluate each of the following limits. 1-V3-x 4) lim x→2 4-x2 5) lim x→∞ 3 Sin ) 2 6) lim(4x +…

A: We have to evaluate the given limit.

Q: 2. Determine the infinite (∞ or -0) limit as follows: x² – 2 - (a) lim x2- x2 3x + 2 - 4-6 sin x – 1…

A:

Q: If 2 - x2 <=g(x)<= 2 cos x for all x, find lim x-->0 g(x).

A:

Q: Determine the limit. 5Tt 9) x→-T/2 lim COS cos (tan x)

A: Given  The limit is

Q: 4. Evaluate the following limits: sin x (a) lim x-0 x³-7x2+10x (b) lim x→2 x2+x-6 sin at (c) lim…

A: Note:- As per our company guidelines we are supposed to answer only first three sub-parts. Kindly…

Q: I. Evaluate the following limits. 1 1 1. lim x – 1 et — е x→1+ - - 2. lim (sin x)tan a x→0+

A:

Q: Find the limit. cos 18x lim X-> 5x 8.

A: Topic = Limits

Q: Evaluate the following limits: x – 25 (i) lim x+25 Vx – 5 Vx² – 3 (iii) lim x→-o 4x +5 sin(50) х — 3…

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

Q: Find the limit. (e-2x cos(x) lim

A:

Q: 1-sin x 18. lim TL X- 2.

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.