- Evaluate only thre tan 30 lim 0 sin 80 x+1 lim X00x2+3 ii. lim,sx.g(x) if lim,s = 2 *+g(x) lim,otsin iv.

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: 5 tan(4x) x→0 3 sin(2x) Evaluate lim using L’Hôpital's rule.

A: The  L'Hopital's rule is: Suppose, f(x) and g(x) are two functions and their limit is given as:…

Q: Evaluate the following limits. 1. lim 1 cosh x x+0+ ln(x² + 1) 2. lim (tanx) (sin x-1) x+7+

A: Let's solve for given limit.

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

A: Rewrite the expression as:

Q: Compute the following: x2-25 lim x-5 i. x-5 lim sin x 1-cos x ii.

A: evaluate the limit in following way:-

Q: 1- cos X lim x→0 1- Prove that

A: As per Bartleby's expert answering policy, we cannot answer more than one question so kindly post…

Q: I. Evaluate the following limits. x sinh x 1. lim x-40 cos 3x – 1

A:

Q: b) If x sin x 2 - 2 cos x hold for all values of x close to zero. Find limx0 xsinx ? 2-2cosx

A: Given, limx→0xsinx2-2cosx

Q: 1. Evaluate the ff. limits: -1 (e*). V1 – e2¤ sin' 2 lim (а) x→0- - 1 - (b) lim x + sin

A: Explanation of the answer is as follows

Q: Q 4. (a). Simplify the indicated limits on the following. 3x2+5 lim x-0 x²+1 + el-*] (i). (ii). lim…

A: 1) =?

Q: -3k sin() - cos(;)| for k = 1, 2, ... and let A = lim y00 A(k). Then Let A(k) Select one:

A: We have defined a sequence of matrix as  A(k) =  - 3kSin(1/k) - Cos(1/k) e^( -1/k2 )  e^( -k2 )…

Q: 1. Solve the following limits. (a) lim 1-0 V1+ x² x In x (b) lim 1400 x + In x 2+ sec (3x) (c) lim…

A:

Q: 1. Determine the infinite (oo or -o) limit as follows: x² - 2 (a) lim x2-x² - 3x + 2 sin x 1 x+ cos…

A: Topic = Limits

Q: Use the identity sin 30 = 3 sin 0 – 4 sin' 0 to evaluate the limit, sin 30 – 3 sin e lim - 03

A:

Q: Exaluate the following limi- 1. lim to + x' xー>-○ x(- 2x2 +5) x° 2. lim sin 3(2x+1) ×ー>-ム 2 2x +1

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: 1. Find the limit (if it exists). (If an answer does not exist, enter DNE.) 2 - x im x² – 4 sin 2x…

A: Find the limit of the given function  1) (2-x)/(x2-4) , when x tends to 2 .  2) sin(2x)/sin(3x) ,…

Q: Can you help me step by step?

A: First move the limit inside tan. So that the limit is on terms with t only.

Q: 12. Evaluate the limit n Σ lim -> sin(- n→∞ N k=1 by expressing it as an integral.

A:

Q: 1. Find the limī lim In(sin x) X→π-

A:

Q: (a) Evaluate two of the following limits: 1-cos ax sin( 1-x² ) tan 2x (i) lim x→0 1-cos bx (ii) lim…

A:

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: 5. Evaluate the following limits: sin(6x) а. lim x→0 5x3-4x cos e – 1 b. lim sin 0

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: Let fn(x) = n²x²(1 – x) on [0, 1]. Does lim,-00 So fn(x) exist?

A:

Q: Q2.) Find the limit ( 1 lim X+x cos x 1. X→ 0 sin x cos x |x + 2| 2 - lim(x + 3) x-2 x + 2 lim sin…

A: solve using properties of limits

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: エ→2ー Prove that lim sin(1/x) does not exist. Lot II

A:

Q: Please I want solution of sub-parts question 5 with step by step. Many Thanks

A:

Q: Find the limit. lim x→4  sin(x − 4) x2 + 5x − 36

A: To Determine: find the limit of  limx→4sin(x-4)x2+5x-36 Given: welimx→4sin(x-4)x2+5x-36 Explanation:…

Q: Can I get help with this question step by step?

A: Consider the provided expression:

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

A: Given  The limit is

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: Q14. The value of lim et3 -x tan x-cos x x2 is? -

A: use l hospital rule for solving for the integral.

Q: If 2 - x s g(x) s 2 cos x for all x, find lim,0 8(x).

A: Given,               2-x2≤g(x)≤2 cos(x), for all x And we have to find,      limx→0g(x)

Q: 1 Prove that lim dx exists and find its value. (1+x?)" 1/2

A:

Q: Q.3/ Find the limits for the following: 1) lim sin 7x 2) lim x0 sin 5x 3) lim V-3 x→9 ズ-9 x1x3-

A: We will find the limit.

Q: -x + 1, x > 0 3) Let f(x) = sin x -,x < 0' (a) Find left-hand and right-hand limits as "x"…

A: we have given f(x).  We have to find the left hand and right hand  limit.

Q: 1-28, evaluate the indicated limit, if it exists. Assume sin x that lim L I sinx 1-0 tan x 9. lim

A: We need to evaluate the following limit if exists.

Q: Express the limit lim > (5 sin(27x; ) + 8)Ax; over [1, 5] as an integral. n→ 00 i=1 Provide a, b and…

A: To find the solution

Q: 2. Find the limit and confirm your answer using the sandwich theorem 1 - cos x lim 818 1. 2. 3. 4.…

A:

Q: 4. Find lim (sin¬ V)cschr. r0+

A: The given limit,         limx→0+sin-1xcschx

Q: 2. find: en(x?) a). Lim メ-1 b). Lim 1 - cos "x 1-COS 4x2

A: