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

Q: (2-4)* Q1: limx-1 sin(x³–1) x-1

A:

Q: Calculate each of the limits in Exercises

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

Q: 9. Lim 6x - Sin 2x メ→0 2x +3sin 4X b. lim x²-1 1/2

A:

Q: ,- 3y sin (4x) - 3y - 2 e sin (4x) Find lim - 4x (х,у)—> (0,0) - 2 e sin (4x) lim - 4x (х,у) — (0,0)…

A:

Q: In(1+x) -x cosx -1 1. lim x-+0 7- In(2x + 3) 3. lim x-00 In(5x -2)

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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+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: Зx2-14х +8 lim 7x-28 x+4

A: By factoring method: Take factors in numerator and denominator  Limx-4(3x2-14x+8)/(7x-28)         =…

Q: Q4: A) solve: 1+xsin 1) lim- y0 1+xcos sin 2) lim -2m 20-4

A: Note: We are entitled to solve only one question at a time. To Find: i. limy→01+xsin1x1+xcos1xii.…

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: tan (2x) 3. 24. lim- %3D .3

A: We replace tan(2x) by sin(2x)cos(2x)…

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: Compute 1) Lim X-3.9טTX 2) um X-71T sin x TT-X 3) um -X. X2-X-6

A: (1) The given expression of limit is

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

A:

Q: (а) 1- cos 4x lim x? x-0 5-х (b) lim- 45 Vx-1-/2x-6 312 -t- 2 lim 1² -1 (с)

A:

Q: 1 COS X 13. lim- ズ→0 14. lim e -3x+4 15. lim 4x+7 ー-00

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: cos(7x) – 3 + b lim- x-0 e2x – bx – 1

A:

Q: 9. - (a) Compute lim I--3 I-3 sin (0) 0 0 2 cos2 (0) -2 (b) Compute lim 1 (c) Compute lim I-0 I -

A: a. limx→3x2-9x-3limx→3x+3x-3x-3  x≠3 ,a2+b2=a+ba-blimx→3x+3=6b. limθ→0sin2θ2cos2θ-2Using L hospital…

Q: By L'Hopital's Rule, X-2 lim x→2 X²-1 1 1 lim. = x→2 2X 4

A: L’Hospital’s Rule: Suppose that  limx→a f(x)g(x)=00  OR  limx→a f(x)g(x)=±∞±∞ where a can be any…

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

A:

Q: 1 Find lim 3 s-2- \s-2 s²–4,

A: Given, Evaluate lims→2-1s-2-3s2-4

Q: H-w in limits 3-3- 2.21 9 iaam ) Lim. 1- CosC2K) Sin (24) 2 - メャ3 2) Lim x2x -3 3) Lim (X+4}-16

A:

Q: (3) Evaluate lim -(1+sin(4))t dt

A:

Q: 3. Find lim x sin II

A: Given limx→∞xsin(πx)

Q: (2) limuy)-(0,0) In(1+x²y®) =,

A: When we put x=0 , y=0 in the function we donot get indeterminant form so we can put the values…

Q: 1 1 7. lim X-0 (Arctanx)² x2

A: Limit is the value of the expression as the independent variable approaches certain value, not…

Q: (4+ 43) (x + 43) -(16 + 43)x limy→ -43 limx. x + 43

A:

Q: cos x-2sinx 1. limx-n 3cosx -2 limx-3 X-3 3x6-x*+2x-3 limy--o 4x5+2x3-5 iv. lim,→-1(x³ limy--1(x³ –…

A: [i]

Q: Q3/Solve THREE only 30 M 6V-6V2x-1 5) lim a+2|-2 sin(x-1) 1) lim 2) lim *-2 3) lim 4) lim 1+2x-3 -1

A:

Q: 11. lim x→ー4 x2-16 2x2+9x+4 z2-36 12. lim Z--16 Z-6

A: (a) We have the given limit problem as limx→-4x2-162x2+9x+4 On calculating the factors of numerator…

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: (2-4)² limx-1 sin(x3-1) x-1

A: by using limit algebra and L' hospital rule

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

A:

Q: Q3) Find: (1) lim, V1+cos 2x (2) lim-2 (x+ 2) 14-x2

A:

Q: 1. Find lim an 3(x+h)-tan 3x A. 3 sec 3x tan 3x B. sec? 3x C. 3 tan 3x D. 3 sec2 3x

A: limh→0 tan3x+h-tan3xh So here fx =tan(3x) Now we need to find derivative of fx with respect to x…

Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of: 1 2 (1) limx-o[: 1-cos x sin²x (2)…

A:

Q: /14-х-3 lim 1-V6-х X→5 4-Vx lim х>16 16-х

A:

Q: Show that lim (x,y) → (0,0) 12 √16x +9y¹ 4x²+3y does not exist. Please show a complete solution.

A:

Q: 13x3sin(는)= 13 2.플) .3, lim %3D (x.y) → (1,-

A:

Q: We have lim I- a Vsing 1-x = (- Fa)(+Ta) So, lim 1- Fa lim - a 거- (1-「 (i+Tx) %3D lim ス→) as 1+ T…

A: Yes your solution is correct

Q: 3. Prove lim 3x-7= 2 X-3

A:

Q: 2 In(x) c. limx→1 1-ex-I d. limr¬0 sin(x)-x cos(2x)-1

A: We can answer both the question as below.

Q: 2x (1) lim x→0 3– vx+ 9 -

A:

Q: 3+2r lim エ→0 =?

A: Given , limx→03x2+2xx

Q: Q2) Find : (a) lim (2 + x) x-4+ 16-x 1-secx 0 sinx cos2x sintx (b) lim (c) lim (d) lim x-0 sin2x…

A: Dear student, According to bartleby guidelines when student post more than one question then expert…

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.