1. Evaluate the following limits. L'Hopital's rule is NOT allowed. 2-√√x-1 1. lim x-5 x² - 4x - 5 2x 3x-4 2. lim - x² = x^2) X-2 |2x - 1| tan-¹(¹) 3. lim 2x - 1 X-2- -0-X

Q: 5x - 10x2-7x lim 5- 8x-5x3 5x – 10x? - 7x 1. %3D 2. lim 5 - 8x 5x3 II

A: I will solve this by taking the common factor out of denominator and numerator and cancelling it.

Q: (x³ - 2x2 - 6+3x) 6. Evaluate lim- X-2 x- 2

A: To evaluate:                      limx→2 x3-2x2+3x-6x-2

Q: 22. lim √x + 6 x 3 x + 2

A: To find :-

Q: If 3x - 4 s f(x) sx2 - 3x + 5 for x 2 0, find lim f(x). x-3

A: Given, 3x-4 ≤ fx ≤ x2-3x+5              for  x ≥ 0 We have to find limx→3fx

Q: xV1-3x lim | V1-4x3 I-00 %3D

A: Suppose L is limit value of given Limt

Q: Find the limits x2 – 4x + 8 lim I -00 3x

A: Given  We need to find the limit.

Q: Find the following limits: lim (x² – 13) a. X--3 b. lim 8(t-5) (t - 7) t-6 2x+5 lim x-211-x³ c. C.

A: To find the following limits.

Q: 2x +1 if x3 (А) -5 в) 6 23 D) -13

A: Here I am attaching image so that you understand each and every step.

Q: Calculate 14. lim (√x² + 1 - x). X18

A: Using series expansion about x =inf

Q: Find the limits a lim X→5 (x2-5x) / (x2-3x -10)

A: limx->5x2-5xx2-3x-10

Q: Evaluate the following limits. 1. lim X->3 2. lim 2 x-q x-3 X-3 X-3 √x-2-√4-X 3. lim (x³²-x²-x-2)…

A:

Q: If limx→.3[x³ + f(x)] = -29, use the Rules of Limits to evaluate limx→.3[36x^² + f(x)- 3x]. O a. 11…

A: limx→-3x3+fx=-29

Q: 19. Evaluate lim (x³ + 2x2 – 3x – 4). x-1

A: Evaluate limx→-1(x3+2x2-3x-4)

Q: Sfsin(r – y kýyd . B. (i) Evaluate 00 sVx+1 lim (ii) Evaluate * 4Vx +3

A:

Q: Find the limits of the functions lim メ>- (6lim x 2. xペー 2x+4

A:

Q: Use the limit laws to evaluate lim (3x − 12)√√x + 4. x→6 Enter the exact answer. For example, enter…

A: given limit

Q: Which of the following statements is true? 7x2 7 A lim 3 (ку) - (0,0) Зx2 — 5ху+ 2у Зx+у-4 lim 8…

A:

Q: 9x¹+x x-100 2x¹45x²-x+6 iv. lim

A: Given limx→∞ 9x4+x2x4+5x2-x+6

Q: Evaluate lim f(x), f(x) = (3x² + 5x − 1, (7x² - 2x - 3, x ≤ 2 x > 2

A: Topic:-  limit and continuity

Q: 18. Explain why a lim √√x-3 X-73 b) lim x²-4 19.) the given x-2x²-4x+4 lim c.) fox)=√5 if x 21 22,…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: As x→ 2+, x? and x2 · 4 → x2 So the lim x → 2+ 4 Therefore, the line x = is a vertical asymptote.

A: Solve the following

Q: Find the limit L. 2x2 + 8x + 6 lim X--3 x + 3 L =

A: Factorise 2x2+8x+6 2x2+8x+6=2x2+6x+2x+6                     =2x(x+3)+2(x+3)…

Q: Find the lim (√9x² + x - 3x)

A:

Q: 5. Find limf(x) x4-3 a) f(x) = 5x4 %3D 6x4 - 3 b) f(x) = 3x3 2x3 - 9 c) f(x) = %3D 3x5

A: We have to find limx→∞fx for a fx=x4-35x4b fx=6x4-33x3c fx=2x3-93x5 Since all above limit has ∞∞…

Q: Find Lim- 3x-6 x-2 x²-4' A. ∞o C. 34 Select one: ос O B О А B. D. +13 010

A: