39. lim 0 cos 0 40. lim sin 0 cot 20 0-0 0-0 tan 3x sin 3y cot 5y 41. lim 1-0 sin &r 42. lim y-o y cot 4y tan 0 e cot 40 43. lim 8-0 02 cot 30 44. lim -0 sin? 0 cot? 20 45. lim 1- cos 3x 2r cos'x - cos x 46. lim

Q: 1 + x + sin x 47. lim 3 cos x 49. lim Vx + 4 cos (x + T)

A:

Q: Number 33

A: Given,

Q: d) lime tan 0 sin 0 3. e) lim0 sin z-cos z+1 3z

A: We have to find the limits .

Q: 1. y = sin(x) tan(x) 2. y = cos (x) 3. y = cos(tan(x)) 4. y = tan(x) A. y' = -3 cos (x) tan(x) В. у…

A:

Q: 3(1 — с cos x) sæ) 64. lim x→0

A: Just use L'Hospitals rule.

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: Increasing and decreasing functions Find the intervals onwhich f is increasing and decreasing.

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

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.…

Q: tan 0 cos 20 7. lim 0→0 sin 20 8. lim 0→T/2 tan 0 sin y 1- cosy 9. lim y→0 sin? y 10. lim y→x 1+cosy…

A:

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: A. Let 0 = 2x, then the identity cos 2x = 1-2 sin2 x becomes cos e = 1–2 sin2 (0/2). a. Use this…

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: 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…

A: 6. Given the limit limx→-13x+1 The limit is defined at x→-1 Therefore the limit value at x→-1.…

Q: Infinite limits at infinity Determine the following limits.

A:

Q: 21 26. lim * Csc 2x o cos Sr 27. lim o tan 2-x + sinx 2x 28. lim ár(cotx)(csc 2x) 30. lim 35, im fan…

A:

Q: Prove the identities sinh (x + y) = sinh x cosh y + cosh x sinh y, cosh (x + y) = cosh x cosh y +…

A:

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

A: The given expression is limx→24x3

Q: 1. If z=ln (x-y) +tan (x+y) find zxx and zyy

A: Given: z=lnx-y+tanx+y  ……1

Q: 4x[ cos (2x) – 1] sin (5x) – 5x Use L'Hopital's Rule to evaluate lim 4x[ cos (2x) – 1] lim sin (5x)…

A:

Q: y = In O it Vsin 0 cos 0 1+2 ln 0 4 0(21n0) In (YS [cot 0-tan 0 another answer 1 1 [cot…

A: Given

Q: i) lim(In (3x– 2)– In(5x+4)) Зх +1 lim 1 j) x0* sin x k) lim (csc x- cot x + cos x)

A:

Q: In Problems 28–44, establish each identity.

A: Trigonometric identities are given, we have to prove the identities. Note: we are answered with 3…

Q: O Lim tanx メーンク メ と5 5+s2 2Lim S+1 ン4 3) Lim 3-→ yリアンチアン49 6+ )Lim I+ Cos メ→

A:

Q: 1. limu→-3 2. limh→0 3. limx→0 u+3 u²+4u+3 √5h+4-2 h 1–cosx x sin x tan 8 4. lime-002 cot 30

A:

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: Q4 1-F(x)=limx→0 vV(x2+3)-3}/x2 2- limy 3y+5y2-7 10y3-11y+12 sin4x 3 - lim 0 sin2x

A:

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)…

A:

Q: cos cos 30 - cos 50 lim- 0>0 s 70 - cos 90 cos

A:

Q: 4 points lim h→0 2h cos(x² + 1)dx O 1 O cos(1) O sin(1)

A:

Q: 5- Show that a) sinh (z + ni) = – sinh z c) tanh(z + i) = tanh z

A: The complex function is of the form z=x+iywhere x is the real part and y is the imaginary part. A…

Q: 1. y=(-1/2)In(e^cotx^2) Find: sqrt of (y')x^-1 2. y=arctan(sin e^x) Find: ((y')e^-x)^2 +tanh^2 (e^x)

A: Now we will find y' and then solve the problem.  Here we will differentiate using chain rule.…

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) –…

A:

Q: 1+3x COS x - 2.) lim tan x

A:

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

A:

Q: lim E(cos (27x;))Ar over [0,5] COS i=1

A: The definite integral is defined as  ∫abf(x)dx=limn→∞∑i=1nfxi*ΔxWhere, Δx=b-an, xi*=a+iΔx The…

Q: AWO Lim tanx L Szx Lim X-CSc メーラク メ メラ。 OLim ()) S→の 6 Lim di6-X +1XI メー→ロ y4 (3) Lim J→ y2ラッチアy49 4…

A: 1. limx→0tan xx2. limS→∞SS+1S25+S23. limy→∞y4y4-7y3+7y2+9 Note:    Multiple parts are given, we are…

Q: Find the limits in Exercises 25–30.

A: we have to find the limits in the given following questions But since we only do the three subparts…

Q: 7. (3 tan x 1 - 2 cos y) sec² x dx + tan x sin y dy = 0. ANE cos y tan² y ton3 y L

A:

Q: Finding LimitsIn Exercises 9–28, find the limit or explain why it does not exist.

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: limit as x approaches 0 of x^6*cos(4/x)

A:

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

A:

Q: not exist". x2 + 3x + 2 (а) lim x-2 x +2 cos O 1 (b) lim 0→0 sin 0 (c) lim In(sin r)

A: To evaluate the following limits: a limx→-2x2+3x+2x+2 blimθ→01-cosθsinθ climx→π+In sinx

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 :

A:

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

A:

Q: find 7. (x, y)→(0,ln 2) In |1 + x² y²| lim et-y 8. lim (x, y)→(1,1) 9. e' sin x 10. (х, у) —-(1/27,…

A:

Q: S lim 1 (1+x)2+n³ cos (nº + x³) dr

A: HINT:  Used Integration formulas and limit formulas.

Q: 9. lim -cosy y>0 sin? y sin y 10. lim y»z 1+cosy sin ax 12. lim x→0 sin bx 11. lim x csc 3 x

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

Q: Limits with Three VariablesFind the limits in Exercises 25–30

A: Dear student, since you have posted multiple questions, as per our policy we will answer first…

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.