Evaluate the following limit sin x lim x-0 (x2+3x) O 1/3 O 1/4 O O

Q: Evaluate the following by limit of su (3x² +5)åx (sin x)dx

A: Solution:To find the integration Formula:∫xndx=xn+1n+1+Csin2x=1-cos 2x2∫cos ax=sin axa+C

Q: Evaluate the following limit. x² + x – 2 lim a-2 x2 + 5x + 6 O A. 3 Ов. O B. O C. 0 O D. -3 O E. 2

A:

Q: Find the limit of the following lim    ln(cos(x)) x→(pi/2)-

A: Consider the given limit.

Q: Q6 Evaluate the following limit using l'Hôpital's rule: (x+1 lim 1 X sin x/

A:

Q: Evaluate the following limit using L'Hospital's rule: 1 - x + ln x lim x→1 1+ cos(3rx) CoS

A: Value of limit is  0 Explanation is given below

Q: 1 lim (cos x)*

A: cos(0) = 1 1∞ = 1

Q: Evaluate the following limits by constructing the table of values. 1. lim 3" 5. lim tan r 0 2. lim…

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

Q: 2. Evaluate the following limits. cos X h. lim-

A: Limit

Q: Evaluate the following limit. sin 5x lim x0 tan 7x

A: Find the limit of a function

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: 3 (b) lim (sin r) In x I 0+

A: We have to find limit

Q: Evaluate the following limit. t lim cos ti-6 sin j+-k 2

A:

Q: Evaluate the following limit. 169 8 + sin x6 lim 3 X00 X +

A: Replace x by 1/t and solve the limit simply.

Q: Evaluate the following limit. tan (3 x) lim x→0

A:

Q: evaluate the following limit lim -Vx+ e +sin(x)cos(x) 1+ In (x)

A:

Q: Evaluate the following limit. t sinj+ sin = 1+ k t -k π lim costi-5 1-x

A:

Q: How to evaluate the attached limit.

A: The given limit is,

Q: Compute the following limits if they exist. sin x - (b) lim x→0 x tan x |

A:

Q: 2. Find the limit of the following function sin(x? – 4) - lim x-0 x - 2

A:

Q: a In x (b) lim 100 I+ In x

A:

Q: Evaluate the following limit. sin(cos a) lim tan x O A. -2 B. O C. O O D. -2 O E. 2

A:

Q: 3. Evaluate the following limit. 1 lim x→0* x 1 tan x,

A:

Q: Evaluate the following limit. Use l’Hôpital’s Rule when it is convenient and applicable.

A: The given expression is limx→πcosx+1x-π2

Q: (c) lim r csc(x)

A:

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 each of the following limits. Тапx-x 1) lim x-0 x-Sinx 2) lim lnx – x² + x x-1 (x-1)2 3)…

A:

Q: x+cos x b) lim x-∞ x3+3x

A:

Q: Evaluate the following limit. t t lim cos ti-6 sin j+ -k

A: Given query is to eveluate the indicated limit.

Q: 1- cos x lim x-

A: Given:     To determine: value of the limit.       Concept: L'Hospital rule:

Q: Find the following limit: lim f(x) X-3 O A. 0 В. 1 O C. -3 O D. The limit does not exist

A: Let's find the following limit.

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

A:

Q: Determine the value of the following limit, if it exists. If infinite, specify either o or -o. (If…

A:

Q: Calculate the following limit: 9.sin(x) lim x +0 10.x

A: Note: Let limx→afx=M, where M is finite and let c be a constant. Then, limx→acfx=climx→afx

Q: Evaluate the following limit. Use l’Hôpital’s Rule when it is convenient and applicable.

A: Evaluate the following limit. Use l’Hôpital’s Rule when it is convenient and applicable.

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

A: It is in indeterminant form so we have to take log on both sides

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

A:

Q: 2. Calculate the following limits: (a) COS x – 1 lim x40 sin x In(1 + x)

A: To find the limit Lim(x tends to 0) [cosx-1]/sinxln(1+x)

Q: lim (1+3 sin r)/=.

A:

Q: Find the following limit where f(x) = 3x2 - 2x. f (x+ Ax) – f (x) lim Az0 Ar

A: Given: fx=3x2-2x To Find:  Value of lim△x→0fx+△x-fx△x

Q: Evaluate the following limits:  lim x→0 sin(3x)/5x^3-4x

A: limit

Q: Find the following limit: lim f(x) O A. 0 О В. О Ос. 3 O D. 4

A: We have to check

Q: ´sin x- x cos x lim x – sin x

A:

Q: Evaluate the following limits by constructing the table of values. 1. lim log x x→1/2 2. lim cos x…

A:

Q: Prove the following limit. ) f(x)=x²+2x+6 where lim, 3 f (x)= 21 >) lim x – x+1=-5 =) lim x³ = 8

A:

Q: Consider the following function. f(x) = 4x² - 2x Find the limit. lim Az-0 f(x+ Ar)-f(x) Ar

A: Where , fx+Δx=4x+Δx2-2x+Δx fx=4x2-2x   Putting in the limit we get

Q: Find the following limit: 7) lim (Ln(x) – x) x00

A: Use the following property to simplify the limit.   Use the formula below, while evaluating the…

Q: 1+x-e* 1-cos x lim x-0

A:

Q: Find the limit. lim x5 In x x-0* O 1 O 5 O-1

A:

Q: - Evaluate the following limit 2 sin z – sin 2r a. lim

A: Evaluate the limit limx→02sinx-sin2xx3

Q: 1. Find the following limits: sin x a) lim- b) limxe*

A: Solve limit as general

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.