1. Determine whether or not each of the following limits exists as a real number or as +oo or -oo. If so, compute it. -2x 2+3t J2-9 (a) lim (b) lim x-0o 1 (c) lim sin x t--3

Q: II. Prove that for each of the following lim (x,y)→(0,0) f(x, y) does not exist. ,2,,2 4. f(x,y) x4…

A: limx, y→0, 0x2y2x4+y4

Q: Determine if the following limits exist: x² + y5 lim (x,y) →(0,0) 1 - cos(x) + y² (a)

A:

Q: Let f(x) = /3r – 10. According to the definition, f'(r) = lim h0 (Enter the limit in reduced form)

A: f(x)=3x-10f'(x)=limh→0f(x+h)-f(x)h

Q: Find the value of a, b, andc such that the limit a + bx + cx - cos(2x) lim x4 exists. a = (Enter…

A: →When limit is of the form 00 or ∞∞ then L'Hospital rule is used.     In this rule, take the…

Q: Which of the following limits has a value 0? In x I. lim II. lim X-0 e* Neither I nor II. O l only…

A:

Q: 1. Find the following limits. 2 sin(2x) – x (a) lim

A: Our Aim is to find the limit of the following expression given below:-limx→0 2 sin (2x)-xx-(i)

Q: Use l'Hôpital's Rule to evaluate the limit. COS X lim -X- 3. 3. O A. -3 V3 O B. C. 2 O D. -/2 1.

A: We have to find limit As per guideline we have to solve one

Q: Compute the following limits, using the [4 -(xn) → 0 Algebraic Limit Theorem,where 1+2xn (a…

A: Let (xn) be sequence such that limn→∞xn=0.

Q: B) Evaluate two of the following limits (Without using calcu 1 1) lim 1-cos2 x

A:

Q: 6. Evaluate the following limits analytically. a. lim 1-4 3x+1 r'- 5x - 6 b. lim 1-6 x - 36 c. lim -…

A:

Q: 1. Determine if the following limits exist: 12 + y? (a) lim (1,y)→(0,0) eª + y² – 1 |

A: Let's find limit.

Q: Evaluate the following limits. lim(Vx? +4x+1-x) a. lim tan (1/x) 1oitonh b. c. lim x cos x->0+ 2

A:

Q: D-the result of the following limit is 1² lim x-0 In (sec x)

A: Let's evaluate given limit.

Q: 1. Evaluate the following limits. - 2 lim a.+2 -4 V2 +1-2 lim b. i+2 t-2 | sin 7r lim c.0 sin 3r

A: As per as our guideline i am supposed to solve only 3 part of question 1 . And f getting solution of…

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

A: Limit

Q: Evaluate the following limits analytically, if it exists. (a) Vx+14 – 1 lim x→-10 2x (b) 5x +7x lim…

A: Given problem:-

Q: Solve the following limit by definition (ii) (4 – 2x, x 1 lim f(x) = 2 if f(x) = %3D x→1

A:

Q: 10. Determine which of the following limits exist and does not exist. a. b. 2 - 2 3x - 9 lim 25 * +5…

A: Note:- As per our company guidelines we are supposed to answer only first three sub-parts. Kindly…

Q: 3. Compute each of the given limits. 1 1 1 1 + 3 2+ 1 a) lim ( x2 cos c) lim n-00 n 2 2+- 2+ 2+ | 27…

A: We have to find given limits.

Q: 1. Use the definitions of the hyperbolic function to find each of the following limits. (a) lim…

A:

Q: Determine the following limits analytically.

A: Given limx→3x2-9x2+42x2-3x-9 By using  a2-b2=(a-b)(a+b)

Q: IS In(x² – 1) 6. Evalaute lim x→0 cos(x) - 1

A: To find the limit of the function we have to find right as well as left limit of the function. First…

Q: 1. a) Compute each of the following limits. i ii ²-25 lim X-5 x+5 lim 5x²-3x+1 x-00 4x²+2x-7

A:

Q: Calculate the following limits using the factorization formula x" - a" = 1x - a21x"-1 + ax"-2 +…

A: To find: limx→2x5-32x-2 Using the formula: xn-an=x-axn-1+axn-2+a2xn-3+.........+an-2x+an-1

Q: Find the limit. За + 5 lim x→0 x – 4 O -5/4 O DNE O 3

A: Limit problem

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

A:

Q: 16. If f(x) = 2x – 1, what is lim x+h h B. - С. —2 D. 2 NIN

A:

Q: For the function 0 < x < 4 = 4 2x – 4, -2, f(x) = x2 – 8x + 20, 4< x use algebra to find each of the…

A:

Q: Evaluate teh following fucntions

A: Dear Students,  “Since you have asked multiple questions in a single request, we will be answering…

Q: Express the limit as an integral (or multiple of an integral) and evaluate.

A: limN→∞3N∑k=0N-110+3kN

Q: Compute the following limits. Algebraically 1 1 3 x cosʻ x-1 (a) lim x→3 x-3 (b) lim identity c) Lim…

A: Using rules of limits.

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: lim x2 - 6х +9 2x -x-21 lim x-3 9-х2 1-sin x lim x- cosx

A: Given: The given expressions are, limx→5x2-6x+9 limx→-32x2-x-219-x2 limx→π21-sinxcosx The…

Q: 1. Solve the following limits. (a) lim T→-∞ V1 + x² x In x (b) lim x UJ + x 00x 2+ sec (3x) (c) lim…

A:

Q: If 1/(x^2 + 1) ≤ f(x) ≤ 1 + x^2 for all x in the interval (−1, 1), what is lim x→0 f(x)?

A: Please refer the attached image for complete solution.

Q: Q4: - Evaluate the limit of the following: x3–1 sin 2x 1-V 1) lim 2) lim x→0 2x²+x 3) lim x→1 1-x…

A: When we get 00form, we can us  L' Hospitals Rule to calculate the limits. In this rule μx→a…

Q: Evaluate the following limits: V10 + 6х — 2 (a) lim x→-1 x2 – 2x – 3 1 – sin(x) (b) lim x→5 (2x –…

A: Use l hospital rule for finding the limit.

Q: b): Evaluate each of the following limits: 1- cos 3x 1)lim x→0 9x2

A: Given, limx→01-cos43x9x2

Q: Find the limits as x - oo and as x » -o. y f(x) (2 - x)(1 + x)2(1 - x)4 lim f(x) 1 X X co lim f(x)…

A: Given,

Q: Prove each of the following limits by intuitive and graphical methods: lim 2r = 6

A: To Prove: limx→32x=6, by intitutive and graphical method. Explanation: (a). Intuitive…

Q: 5. Evaluate the following limits: eh-1 a. limp→o 2h а. b. limx→1 1. x2-1 1 c. lim,»∞x tan d. lim,→1…

A: Since you have asked multiple questions in a single request, we will be answering only the first…

Q: 1. Evaluate the following limits: x2 V2x2 + 1 Vx2 + 5 (a) (3 marks) lim (b) (4 marks) lim a→3 2* +…

A:

Q: Find the limit. 2 )X lim 1+ x4 O A. O О В. 1 O C. 0 O D. 2

A: We have to find

Q: b): Evaluate each of the following limits: 1- cos* 3x 1)lim x→0 9x2

A:

Q: 4. Evaluate the following limits: sin x (a) lim x-0 x³-7x2+10x (b) lim x→2 x2+x-6 sin at (c) lim…

A: Note:- As per our company guidelines we are supposed to answer only first three sub-parts. Kindly…

Q: Evaluate the following limits by constructing the table of values. 1. lim -cos(3t) 3t t--0 f(t).…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: 13. lim )- (2- x→2 4-x Vx+7-J7 14. lim x→2

A: (13) We have the given limit problem as, limx→22-x4-x On calculating the factors of numerator and…

Q: 1. Evaluate the following limits. x² + 3x+ 2 lim, →-1 x' +4x +3 2 а. х? — 2х lim,→2 b. Vx? +5 – 3

A:

Q: Determine the following limits at infinity. f1x2 xSo g1x2 lim if f1x2 S 100,000 and g1x2 S 00 as x S…

A: Given information: The function f(x) approaches 100,000 and g(x) approaches infinity as x approaches…

Q: 27 Let f(z) = エー3 Find lim f(r). Enter I for oo, -I for - 00, and DNE if the limit does not exist.…

A: In this question we have to find the limit of the given function.