6. lim 3**1 16. lim sin 9x 7. lim 2-1 17. lim 0 sin 10x tan ax 8. lim In(x +x - 1) 18. lim 9. lim In(x -x + 1) 1-cos x 19. lim o tanr 10. lim In(x+2) 20. lim 5 cos a-s o sin Ba

Q: Find the limits in Exercises 39-46

A: Since you have posted multiple questions, as per our policy we will answer first question. Please re…

Q: 4. lim 2 sin 0+6

A: limθ->-∞2sinθ+6 We know that the range of sin is from -1 to 1 sin 90 is 1  and sin (270) is -1.…

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Q: 8 sin 3+ 5/ is equal to The number lim | sin(x) dx E. 5. 8 sin(x)dx 8 | sin(x) dx 3. 0 8 8. sin(x)…

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Q: 2x[ cos (3x) – 1] sin (6x) – 6x Use L'Hopital's Rule to evaluate lim 2x[cos (3x) – 1] lim sin (6x) –…

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Q: Finding LimitsIn Exercises 15–28, find the limit or explain why it does not exist.

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

Q: 1 o. = 0. Show that lim x² sin -| *

A: Use the property that -1≤siny≤1. Take y=1x, then -1≤sin1x≤1

Q: 12) Solve: (tan x) (2cosx+1) = 0 %3D tan x = 0 2 cos x + 1 = 0 x = 0 2cos x = -1 m<x= 0 coS X = - m<…

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Q: 14. lim cos x 15. lim cos(x+ sin 16. lim

A: If any function is continuous within a given interval, then its limit must exist in that interval.…

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

Q: find the one-sided limit

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

Q: lim sin(k/n). 1. cos(1) +5/3. 2. cos(1) +1/3. 3. cos(1) +2/3 4. cos(1) – 1/3.

A:

Q: H.W 1: Prove cos 4x = 1-8 sin² x . cos' x H.W 2: Prove that: sin 2x cos 2x sin x cos x sec x sin ( a…

A: 1) Prove that cos 4x=1-8sin2 x ·cos2 x. Consider the left hand side. cos 4x=1-2sin22x…

Q: Prove the identity. 1+ tanh(x) = e2x 1- tanh(x) 1 + cosh(x) 1+ tanh(x) 1- tanh(x) 1 cosh(x) cosh(x)…

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Q: True or false: If tan 3x = any integer n. + nn for 4 1, then x = %3D

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Q: n+1 Evaluate lim cos“(x²)dx n→∞ (and show all work)

A: The required results are as follows: cos2 x=12+12·cos(2x) and cos 2x=1-(2x)22!+(2x)44!-(2x)66!+...…

Q: find 49. lim 0 - sin 0 cos e tan 0 - 0 sin 3x - 3x + x² 50. lim sin x sin 2r

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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: 22. lim cos2 (x - tan x) cos 2x - 1 sin x 24. lim

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Q: Infinite limits at infinity Determine the following limits.

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Q: In Problems 7–16, use a table to find the indicated limit

A: The given expression is limx→24x3

Q: Find the limits

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Q: 4) lim (1 + sin 4x)¹/x x→0+

A: Given limx→x+1+sin(4x)1x

Q: 9. lim e 10. lim e* x+00 x00 sin 6x 11. lim 5*+6 12. lim x+00 1 13. lim COS X 14. lim e -3x+4 4x+7…

A: These questions are related to limits, we will solve them using given information.

Q: |- lim メ→ X-3 2. lim メ→2 (会 4 メー2 メ*-4 3. lim メ→。 3メ - S;u4X 4. lim メ→。 tau3X 5- lim 1- Cose Sin'e

A: Since you have asked multiple questions. So, we are solving first few for you. If you want any…

Q: x²+3 1) lim X00 x2+4 1-cos x sin x 2) lim- X-0 sinx 3) lim X-0 ex-1

A:

Q: x² +9 √(x² - 1)(x^² + 4) In 1x + 11 + In |x-1| + tan-¹) + C Option 1 In x +11+ In |x-1|-tan ¹ () + C…

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Q: Vx 6. lim x00 In(x1000) 7. lim 3*-2x X0 x2-x 8. lim 35 sin (nx) cos2 (Tx) 9. lim X-5 2n2(x-5)2

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Q: x + sin 2x lim x-2 x – sin 2x О з O 2 O 1/3 О 12 O other:

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Q: (1) lim (In ) = z (x1 (j) lim rsin z x→0+ sin 2x + 2 arctan 3x + 3x2 (k) lim x→0 In (1+3x + sin? x)…

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Q: Limits at infinity Evaluate the following limits.

A: "Since, you have asked a question with multiple subparts, we will solve the first three for you. If…

Q: 1-sin 0. (5) lim cos.20 (x2-2х+1)50 (6) lim X-00 (х+5)100

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Q: Theory and Examples

A: limx→02x23-3cos x

Q: x² + 9 dx J x2 – 1)(x² + 4) | In \x + 1| + In |x – 1| +; tan-1 (-) + c -In |x + 1| - In |x – 1| -;…

A: Topic:- application of integration

Q: 1-cos 5x cOS lim 6x

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Q: sin 0 – cos 0 lim 0→x/4 tan0 – 1 2(cos x)2 + 3 cos x – 2 lim 2 cos x – 1 y In y – y lim y»e In(y5) –…

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Q: 4.x (a) lim 10 sin 5x sin() (b) lim 5x sin 3x (c) lim 10 x2 tan 2.x

A: Read the following instructions once 1. Short method is provided at the end of the subpart (c)…

Q: 1– tan(*,) [1– sin x] lim 1+ tan(x (¥2) [z – 2x] x- - 2 1/8 1/32

A:

Q: 1- tan lim 1– tan(*,) [1– sin.x] sin x] (2, x→| (¥2)[[7 – 2x} n – 1+ tan(x 1/32 O 1/8

A: The given expression is limx→21-tanx21-sin x1+tanx2π-2x3.

Q: 2x + Vx x² + 4x 3 1. lim 2. lim 7x2 + 2 sin x 3. lim x→-o x + e* 4. lim et 2xe2x In x 6. lim 5. lim…

A: To decide whether the given limit produces an indeterminate form6. limx→∞lnxx

Q: lim,-o-cos(2.x) →0°sin²(3x) Q6- Evaluate:

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Q: 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

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Q: 47. Let y = sec-x. Show that tan y = vx? – 1 if x > 1 and that tan y = -Vx? – 1 if x 0 on (0, 3)…

A: Consider the function of x and solve further-

Q: 1. Evaluate your classmate's work computing the for (고-16)2(1-co82 (풍)) (i) lim -2 (sin (플))(x4-8r2+…

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Q: sin(k/n), lim is 1. cos(1) +5/3. 2. cos(1) + 1/3. 3. cos(1) +2/3 4. cos(1) - 1/3.

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Q: tan(3z) lim 5z z-0 sin(n)(1-cos(h)) lim h-0 sin(h)(1-cos(h) lim h-0 h3

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Q: 1. Evaluate 2. Evaluate sin(20) 30 x-2x cos x sin x limo lim, 0

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Q: (2) elnx = x (1) sin-1x = V1-x2 (1) ax A- Show that : cos x (2) lim x- cosx (2) (1) limx-0 В- Find :

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Q: Limits with trigonometric functions Find the limits in Exercises 43–50.

A:

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.