2. * Question 28: ( Find lim oVx + x + 1-x Find lim co x* + x+ 1 -x) (2) (a) (b) 1/2 (c) -1/2 (d) 2 (e) -1/4

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: prove that lim [x19 cos (1/x2)]=0 x->0

A:

Q: lim (In(x))½ ?

A:

Q: Show limn→∞(1 +1/2+1/3+···+1/n−lnn) exists

A:

Q: Compute the indicated limits. 5x + 5 lim cos 2x2 – 3x – 5 ||

A: topic - limits

Q: 9- Solve the question. Lim cos(2x)/x X->T

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: 35. Use the Squeeze Theorem to show that lim,-o (x² cos 20TTX) = 0. Illustrate by graphing the…

A: To show that: limx→0x2cos20πx=0 Using Squeeze Theorem:…

Q: 3-Vx+3 6. (10) Find lim analytically (if it exists). X→6 X-6

A:

Q: 1- cos(2x) lim x→0 х-0 1 — сos(6х) 7* – 6* – 1 lim x→1 х2 — 1

A:

Q: 1 Use l'Hopital's rule to evaluate lim 1+0+ \I In(1 + x),

A: Question is solved.

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 ** Evaluate lim - X+ oL dt A B none of these 1- e? 1 4

A: Given that,  Now taking the integral term,

Q: Can you solve number 23

A: The given expression:

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: 1 1 Use l'Hopital's rule to evaluate lim x→0+ In(1+x),

A:

Q: 1- cos x lim 1- Prove that = 0

A: According to guidelines we should have been able to solve only one question at a time #1

Q: 1) @) Prove that lim an= o if lal <1 and a ER 6) show fon any X with Ix) <1, lim nxn=0- that

A:

Q: 1- Evaluate the limit a-Limx²-4/(x²-x-2) X-2 b- lim [In(cos(x))]* c-2-(X²+4) ¹/2²/sin²x x-0 x →0

A: L'Hospital rule:- If a function is of the form p(x)q(x)   then if limx→a p(x)q(x)  is of 00 or ∞∞…

Q: In (1+x)-x lim- 1- cos x x-0

A:

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

A:

Q: 4. Use L'Hopital's Rule to find (a). lim 22-In 2 3+2z

A:

Q: Please solve asap my deadline is very close

A: We need to find limx→+∞sinx-4cosx+33x2+cos2x Consider:…

Q: 2 Prove that limx* cos== 4 = 0. %3D - x→0

A:

Q: 2 for al 2 0. 39. Prove that lim x* cos %3D -

A: Given,

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: 5. Use L'Hopital's rule to evaluate e* +2 limy-o ex +

A: limx→∞ex+2xex+5x

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: ()- In(x) C. lim %3D

A:

Q: 12-x-x 1- Prove that lim -7 %3D x-3 V6+x-3

A: our objective is to find the limit

Q: 4. Evaluate lim (cos x)¹/x². x-0

A:

Q: #1. lim t-tvt 213/2 12 +3t – 5 t→ 00 #2. lim x → - o0 x' +1 #3. lim tan1 (In x) x → 0+

A:

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

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: 2. (a) lim T-cos e (b) lim. -70 In R tim (0) メーール

A:

Q: lim cos nл| 2n-1 - 2n+2

A: Use : cos x =1-x22!+x44! + ...........

Q: 1 Find lim dt

A: The given data is: limx→∞1x∫1xdtt  To find the value of the limit.

Q: 6.) Use Theorem 4 lim x csc 3x e 7.) Use Theorem 4 lim e -0 sin? e

A:

Q: 2. Show that lim (x,y)→(−1,0) (x + 1)² sin y (x + 1)4 + y² does not exist.

A:

Q: Prove that lim x cos 4 = 0. X-0 -1 s cos(4/x)s 1 = -x s cos(4/x) s x*. since lim (-x*) = x-0 and lim…

A:

Q: In(3x) EXAMPLE 3 Calculate lim SOLUTION Since In(3x) → o and → o as x - o, l'Hospital's Rule…

A: Given:         limx→∞ln3xx3 L'Hospital's Rule:         limx→cfxgx=limx→cf'(x)g'(x)  Since ln(3x)→∞…

Q: 1. lim ux-121 X-3

A:

Q: In cos 5x Find lim x-0 In cos 4.x

A:

Q: 17. Find limx cos (4) using Squeeze Theorem. x-0

A:

Q: 1. Prove using e-d definition. (d) lim (4x + 3) = 7 x→1 x2 – 9 = 6 - (e) lim x→3 x – 3

A: To prove the limit using epsilon-delta definition

Q: (b) Use the sandwich theorem to show that limy0x°cos - = 0. 1 In order to apply the sandwich…

A:

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

A:

Q: 1. Use L'Hopitals's rule to find lim c In(e" – 1). |

A: limx→0+ xlnex-1

Q: Q show that lim %3D メ→ 0-1

A: We have to show that limx→0.11x=10 L.H.S : limx→0.11x           =10.1               (plug in the…

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.