2r + 3 2r² + 3 41. lim I-00 x + 7 42. lim X--0 5x + 7 - 4x + 8 Зх3 1 44. lim I-00x? 43. lim 7x + 1 x² – 7x x* + x³ 45. lim I--00 X + 1 46. lim 1-00 12r + 128 (If you have a grapher, try graphing the function for –5 sxs 5.) (If you have a grapher, try graphing f(x) = x(cos (1/x) – 1) near the origin to "see" the limit at infinity.) sin x 47. lim 48. lim cos 0 - 1 x + sin x + 2V x + sinx x2/3 +x! 50. lim I-00 x2/3 + cos?x 49. lim 51. lim el cos - 52. lim In(1 + 53. lim tanx 54. lim e sin-!

Q: Determine whether the statment is true or flase.

A:

Q: In(5x-9) lim x2 x3-8

A: For the following limit problem,

Q: lim 1 t-> +→> -∞0 17 + cot = ² +

A: note that cot^-1(- infinty)=0

Q: Find the limits in Exercises

A: We have to find limx→∞e2xsin2x. Let L=limx→∞e2xsin2x. Since x→∞. Therefore, 1x→0. Let 1x=y. When x→∞…

Q: Find the limit.

A: The given limit is, L=limx→2+e32-x=limx→2+e-3x-2

Q: fim 1 t->-∞ 1 + cot = "= 8

A:

Q: Section 1: K/U Multiple Choice: [5 Marks] 1. The lim x->4-7 a) 4 - 2. The lim x-4+ √x² – 16 a) 0…

A: The objective of the question is to test the understanding of the concept of limits, continuity, and…

Q: Prove that lim (2a2 + 3r + 6) = 5 using the e, 8 definition of a limit. %3D a -1

A:

Q: Find the limit HI6) im [In(2 t+x) - In(1+x)] www

A: We will find the limit.

Q: Section 1: K/U Multiple Choice: [5 Marks] 1. The lim x->4-7 a) 4 - 2. The lim x-4+ √x² – 16 a) 0…

A: all answers are explained below in detailExplanation:10)11) The average rate of Change and the…

Q: Find the follawing limits: 1. lim tan" メーbo 2. lim Sith)2I 3. lim 2x-3 メー 7X+4

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

Q: lim In (x°) x2

A: We have to evaluate the given limit.

Q: Find the limit. 5) lim /2x + 5 5) x-6

A:

Q: If we approach c from only one side, then we have a(n)____limit.

A: If we approach c from only one side, then we have a(n)____ limit.

Q: Find the limits in Exercises

A: Given: limx→∞x57+x-3x57+cos x   ……1

Q: Find the limit.

A: Given Data The given limit is:     Substitute the 5 for the x in the equation of limit,

Q: Exercise 2: Mastery Learning Game Directions: Evaluate the limits of the following: 1. lim X--1 ( 5)…

A:

Q: 5. Let x X for n-1,2,3,.... Then lim "n+ n- X n" n A) e B) e2 C) e D) e E) 1

A: First we plug expressions for x_(n+1) and x_n in the given limit.

Q: lim el -1 dt 61-12-e

A:

Q: Find the limit. lim a. 32 b. 24 c. 48 d. 128 e. 64

A:

Q: Calculate limits using the arithmetic of limits: -n+2 n-+00 12² +2 2n²+1 1-400 1² <-n a) lim b) lim

A: Limit:It is the value that a function , approaches as the input x, approaches some value.

Q: 3) lim X→-1- A) ∞ 5 x² - 1 B) -1 0 D

A: Limx-(-1)-1 [5/(x2-1)] [5/(x2-1)]

Q: You want to find out how sleep deprivation affects motor performance. To study this, you have…

A:

Q: Find the limit: x-5 lim x-14 -x+14

A:

Q: fnd the limits ia fovomng exercises: Lim (2x++5) ル→ーネ + 4X+8) *-2 lim y+sy+6

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

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.