sin 5x Evaluate lim x→0 x² – x [Hint: Factor the denominator.]

Q: 1 Evaluate: lim sin2(x) 4 TC 6 6.

A:

Q: 50. Calculate lim, sin(). (Proof is not required) n+2 n-+3

A: We have to calculate the limit limn→∞sinn+2n2+3

Q: x łan 5x sin? (2x) lim

A:

Q: To compute lim,_30+ (sinx) (In x), first re-write in which form? sin æ A. lim,0* īn z In a B. lim,0'…

A: Given that: 1. f'' at critical points.2. limx→0+(sinx)(ln x)

Q: tan(4 x) lim x>0

A:

Q: 1 Evaluate the lim sin x>0

A:

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

A:

Q: 1. x² tan( + 47) + 2 tan-1x lim =? (a) 1 (b) -2 (c) -1 (d) (e)

A:

Q: {) Lim 1-cos Scos2x 7 メー)○ x2

A: Given: limx→01-cosxcos2xx2 for evaluating given limit, we use L hospital's rule according to L…

Q: 6 3x° sin Evaluate: lim

A:

Q: 3. A function f(x) satisfies the inequality 1-<f(x) < 1 + tan² x, when x →0. Using the Sandwich…

A:

Q: Find the value of Tx³ + 2. lim [sin x3 + 1 -1 1 O O

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

Q: Evaluate lim (sin z)an. 10.

A: **As per our guidelines we are allowed to answer only one question at a time. Kindly please re-post…

Q: sin 7x If f(x) = complete the following table and use the results to predict lim f(x), if it exists.…

A: The function is fx=sin7xx.   For x = -0.1. f-0.1=sin7-0.1-0.1=-10sin-0.7=6.442   For x = -0.01.…

Q: III. Use Squeeze Theorem to evaluate lim 8478 COS X log x

A: To Evaluate: limx→+∞cosxlog12x by using squeeze theorem:

Q: tan 5x Evaluate: lim A. -5 X-0 sinx В. -1 С. 1 D. 5

A: There two results of the limit  If  limx→0tan xx , then  limx→0tan xx = 0  If  limx→0sin xx , then…

Q: et - e- е limr0 2 sin x

A:

Q: sin(x²) x→0 In(cosx) 4. Evaluate lim

A:

Q: 2x lim x-4 Vx - 3 LN =

A:

Q: (a) lim 1-cos() 3x (b) lim xe 1/x (Hint: xe

A:

Q: 1 Evaluate lim 1 sin

A: The given limit is limx→∞1sin1x Let x=1/z z=1/x when x tends to infinity z tends to 0

Q: tan(x) d. limx→ x-5 e. limr→∞ xe-*

A:

Q: Find values of a and b such that sin 3x + ax + bx³ lim = 0 x3

A:

Q: sin(3x – 3) lim x² – 1

A: Given :

Q: (iv) Find lim r 2ª – x² sin

A: Limits

Q: (sin x)(15x4 – 5x + 8) Let f(x) = 4x Find the value of limr→0 ƒ(x), or state that it does not exist.

A: Given f(x)=sinx(15x4-5x+8)4x

Q: e – e-* lim I-0 x2 + 3T

A:

Q: sin(5x) Evaluate lim X→0 2х

A: lim x→0 ( sin5x)/2x   We know that Lim x→0  (sin x) / x = 1   Lim.    5/2 ×    ( Sin 5x ) /5x x→0 ​=…

Q: tan3x lim 20 In(1+ x)

A: limx→ 0tan3xln1+xApplying L'Hopital rule=limx→ 0sec23x· 311+xPut x=0=sec23· 0· 311+0=3

Q: Q2: Evaluate: [1] 21 lim m COSXVI+ COSX – v1-x, sin-1(x) V1+x - [3] lim-o

A: Limit of a function determines the continuity of a function. Three types of limits exist, one is…

Q: 1-x c) lim- x1 1-Vx 121 sin x d) lim (Hint: Use a calculator to make a table.)

A: c) limx→11-x1-xd) limx→0sin xx

Q: sin 14x 27. Let L = lim х sin e 14x, that L = lim 14- (a) Show, by letting 0 (b) Compute L.

A:

Q: 1 1 X sin x+sin 2x Q3/ Find the value of (x) if5 -2 1= lim 3x -1 1

A: See the attachment

Q: sin(2x) if x +0 f(x)%3D{ 3x if x-0 17 - lim f(x)+ f(0)=1 find the value of 'c'.

A:

Q: sin 2x tan 3x (a) lim

A:

Q: 1 -is 2 + sin x The value of lim a) 1 1 b) c) 0 d)

A: "Since you have asked multiple question, wewill solve the first question for you. If you want any…

Q: -2x – 1 Find lim X+0 sin 3 sin()

A: Using formulae of limits

Q: sin x 3. Prove that lim :1

A: To prove: limx→0 sin xx=1   Theorem Used: Squeeze theorem: If f(x) ≤ g(x) ≤ h(x) and limx→a…

Q: 4 sin(x - 2) x→2 3 ln (3x – 5) Evaluate lim and write your answer in simplest form.

A: We can find the limit in the following steps.

Q: sinh x Evaluate lim et

A: We have to find limit of given function limx→∞sinhxex We know, sinhx=ex-e-x2 limx→∞sinhxex

Q: Let 2x – 4+ 3() x > 1 f(x) = 8 tan- (ax) x<1 be given. If lim f(x) exists, find the value of a. x-1

A: Given,           f(x) = 2x - 4 + 3x1 - x2;    x &gt; 18πtan-1ax          ;    x≤1

Q: 9 sin 4x lim ] (Type an exact answer.) 5x

A:

Q: Evaluate lim sin(x)(x +2) 4 8 3x/2+8/2 8 O Does not exist

A:

Q: limr→(1 − )tan =N x

A: Concept: Limit of a function: Think about the f function (x). X must have values ​​close to the…

Q: a + cos bx Find all values of a and b such that lim -1. x2

A:

Q: e* + e-x – x² –- 2 lim sin? x – x2 х — x→0

A: To evaluate: The limit limx→0ex+e-x-x2-2sin2x-x2. Calculation: Use L'Hospital rule to evaluate the…

Q: 10 sin(4x³) 12x8 lim X→0

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

Q: 12 sin( In x) (b) Evaluate lim,→1 3+5)(x-1)

A:

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.