lim x->-7  (-x-7)/(4-√(9-x)) lim x->-infinity (√6x^2 - 2x)/(x+8) lim x->0 (7x cos x + sin 5x)/3x

Q: lim (1-cos x1/2) / ln(1+x) ? x-->0+

A: Here we use the series expansion of the functions cos (x) and ln(1+x):

Q: x²-sin²2x 2) lim x-0 x² 4) lim(1+x) cScx x-0

A:

Q: 9. Lim 6x - Sin 2x メ→0 2x +3sin 4X b. lim x²-1 1/2

A:

Q: 3x+7 sin2x x+x.cosx 1- lim- x2-2 lim 2x2+x 3 - lim- x→0 2 - 00+X x→0 sinx.cosx 1 lim x-1- 1-x2 x-3…

A:

Q: lim 1- cos () X00

A: Given, limx→∞1-cos1x To Find the value of this limit function.

Q: limx-->0 sin3x/ex-1

A:

Q: sin 5x 1. limx-0 2x2 +3x 2. limx→0 x3+x+1

A: 1).limx→0 sin 5xx2).limx→∞ 2x2 +3xx3 +x+1

Q: 1. limx→1 x-/2-x2 x4+3x3–13x²-27x+36 2. limx-1 x²+3x-4 3. lim,1- V1 – x 3x3-x²+1 lim

A: In this question we will use basic of calculus I.e concept of limits. Solution of the above question…

Q: 1-sinx x-1-cos2x 9) lim 10) lim TC X- sinx-cosx TL X- 4

A:

Q: lim 2x2 + 7x +5 X-> -I x+1 lim 16 (Titx -1) | Xー76 lim 2x 3-54 X-7 3 X2-9 lim スーフ4 Nin -(ニル) x2-16…

A:

Q: ((주)' lim x (1- cos () COs X->- 00

A:

Q: 1. lim(2x – 5) x+4 2. lim(3x + 8) x-1 3. lim *+1 X-2 x-5

A: Disclaimer: Since you have posted multiple question, we will be solving first three. In case you…

Q: cos x lim X-0 x2-x+3 lim 1-vx-6 x-7 x-7 X+7

A: We have to find out limit

Q: 16. lim (2 – 3x) = –4 x → 2 %3D - 19. lim (1-3-) -- 3 20. lim 2 = 7 x → 5 21. lim x2 – 2x – 8 = 6 x…

A:

Q: lim x----->0    sin x sin 2x/1- cos x

A: Given:-  limx→0  sinx  sin2x1-cosxTo find:-     value  of the above limit.Concept:-  Use 'L Hospital…

Q: 1-cos 2x lim x2 sec x-tan x lim X→0 X→- 2 x- 2 x2 +sin 3x lim 2x+tan 2x . х-0

A: We are solving first question for you. If you want solution for any other question than please…

Q: (2) lim 12 X+6 (3) lim (2x³ – 3x² +x) x3 - 2x2 +3x-5 (4) lim X2 3-x

A: Hello. Since your question has multiple parts, we will solve first three complete questions for you.…

Q: sin(3 – x) lim с2 — 5х + 6 x→2 x2 – 5x + 6

A:

Q: Lim 1- Cosx て X-)0

A: Given: L=limx→01-cosxsin2x We know that 1-cos2x=2sin2x…

Q: x2-4 1) lim x-2 x-2 sin 2x 2) lim 1 1 3) lim(-- X-0 x VX

A:

Q: Indeterminate Forms 1. limx -> 0  sinx / x 2. limx -> ∞  5x3-4x+3 / 2x2-1

A:

Q: imit as x approaches infinity of (1-x)/(3n+5)

A: From the given problem: limx→∞1-x3x+5 As we know that: limx→afxgx=limx→afxlimx→agx

Q: 1. lim (3x + 2) X--3 2. lim(1-x2) -2x2+ 4) X-1 3. lim(3x

A:

Q: 2x2 – 12x 1. lim 1-6 r2 +x - 42 3- V25- 2 2. lim 1--4 r+4 3. lim

A:

Q: 3/x – 3 (k) limx→-∞ 5 - x x³ +1 (1) limx→-∞ Cos -0- x6 +x5 + 100

A: For (k), We need to find limx→ -∞ x-35-x3. So,            limx→ -∞ x-35-x3We know that,…

Q: sin² (x) x…0 COSX-1 7) lim cotx + CSCx X-T 5) lim cosx+1 6) lim X-7 sinx 8) lim(--)

A:

Q: 4-X 1) Lim メ→4 5-x²49 2.

A: To evaluate the below limit. limx→ 44−x5−x2+9

Q: 4. lim (x-5x-2x-x + 100) ズ→ーの x+6x 5. lim X00 3x -5 25x2-8 6. lim ズ→の 4x-5

A: limx→∞ describes what happens when x  grows without bound in the positive direction and limx→-∞ is…

Q: 11. lim x→ー4 x2-16 2x2+9x+4 z2-36 12. lim Z--16 Z-6

A: (a) We have the given limit problem as limx→-4x2-162x2+9x+4 On calculating the factors of numerator…

Q: 47. lim -4 3x-5x +7 8+2x-5x 2-2 48, lim 49. lim

A: we have to solve given problem;

Q: lim 4 square root x -3/x-81 x-->81

A:

Q: x2-4 1) lim x-2 x-2 sin 2x 2) lim 1 3) lim(-- x0 x V

A:

Q: (1) x3 – - 13x + 12 5- V4 + 3x lim lim x-3 x3-14x + 15 (3) 7- x x-7 2x*- 6x3 + x2 +3 2x2 - 3x lim…

A:

Q: 1. lim (4x – 7) 2. lim (x3- 2x² + x - 5) X-1 3. lim (x2 - x + 3)(2x – 1) X-2

A: 1. limx→04x-72. limx→1x3-2x2+x-53. limx→-2x2-x+32x-1 Note:     Multiple sub part are given, we are…

Q: x3–1 х-14x3-х-3 1) lim sin 2x 2) lim x→0 2x²+x 3) lim 1-v х-1 1-х

A:

Q: Lim e^x +e^-x-x²-2/sin²x-x² when x approaches 0

A: The given limit is, This limit is in 0/0 form, so we can apply L’Hospital's rule,

Q: 1. lim(8 - Зх + 12х?) x-2 6+ 4t 2. lim t--3 t²+1 2x2-17х+8 3. lim x-8 8-х

A:

Q: sin-1(x) – tan-1(x) lim 3x3

A: The given limit involves inverse trigonometric function as well as cubic function and the limit is…

Q: sin(3) (x – 6) – 3sin(x – 6) lim x-6 (x – 6)2 + 2(x – 6) + 3 – 3e*-6

A: We have to find the limit.

Q: x2 – 2 3. lim x→2+ [x – x | x2 + 2x 4. lim x→0 x2 2.x - x2 5. lim x→2 10x + 16 - x2 – x – 2 - -

A:

Q: 91_در lim 2-3 z²+4z-21 LIMIT VALUE: lim 2--1 LIMIT VALUE: lim (x³ +7x² - 2x + 4) 2-2 LIMIT VALUE:…

A: Solved below

Q: 19.) lim X+2 X+-2 X ³³+8 3 tiran

A: To find limit of the given function as x approaches to -2.

Q: 1.) lim 3* x-2 2.) lim (2x+¹ -3) x-2

A: Given: 1.limx→23x2.limx→22x+1-3

Q: \lim_(x->-\infty )(x^(2)+ x - 5)/(1-2x-x^(3))

A:

Q: sin(3 – x) lim x→3 x² - 5x + 6

A:

Q: lim sin2x/ x            x--->0 lim tanx/tan2x       x---->0

A: Multiplied the numerator and denominator by 2When x->0 then 2x->0Answer: 2

Q: 1-cos(2x) limx→0 sin² (3x) tan x-sin x lim - Evaluate: а- b- x→0 sin³x

A:

Q: Lim x---> infonity positive 4x^3+x^3-1÷2x^3+5×-1

A:

Q: 2-27 1- lim X-3 2-9 2-2x2+1 2- lim -0 -2 Vx+25-5 3- lim sin2x? 4- lim x-0 x sin x 5- lim X-0 2-2cosx

A: 1.

Q: 1 lim(x²-3x+1) 3. lim tan(x²) 7. lim 2²-1-2 x²-4

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

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.