6. lim x-1 (x3+2x2+6x+5, 2x2-х-3 ALLO AND OMMLEDAND DITED BY 7. lim PLED ANDEDITEDB PILED ANDIDITED COMPLED ANDEDD JUSTO UGUSIO COMPILED AND FDIT AUGUSTO x4 x-4 AUCUSTO COMPILED AND sin(12ß) 8. lim O COMPLED ANDED B0 sin(4B) USIO COMPILED AN STO COMPILLDA STO. COMPS CON USIO COMPILES

Q: (с) 4у" + у %3D 4 sin(3x/2), for 0 <x <л, У (0) %3 0, у(л) — 0

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Q: (a) Apply the Comparison Theorem (Theorem 5 in Section 5.2) to the inequality sin x 0) to prove…

A: Given: Use the inequality  sinx≤x   (valid for all x≥0)To prove:a) 1-x22≤cosx≤1b) x-x36≤sinx≤xc)…

Q: 12 and x terminates in 13 nd sin 2x, cos 2x, and tan 2x if sin x= sin 2x cos 2x %3D tan 2x %3D II

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Q: a) By expanding sin(2x+x) using double angle formulae, show that and sin 3x = 3 sin xr-4sin x.…

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Q: 00 How were sin(x) = [° (−1)²₂2k+1₁ -X these values generated from k=0 (2k+1)! (1) (0) n=0 n!

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Q: 63. First, observe sin 4x = 2 sin 2x cos 2x = 2 sin 2.x(1 – 2 sin? x) = 2 sin 2x – 4 sin 2x sin² x =…

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Q: 2) DISCUSS The Contmuyo f Sin TX %3D

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Q: - 75ec 3x+tan 3x(sec 3x+tan 3x) cos 3x dx (7sec 3x+tan 3x)In 7 + C 7secax+tan ax + C 7 In 3 3 O c B…

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Q: dr 4+x² S Choices: tan ¹(x + 2) + C 1 In x² + 4 +C In x + 2+ C 1 tan 2 1 ¹ 1/2 + +C

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Q: Prove that L (sin² x 2/3 ; p} = 1/ 108 р x (1²,5 + 4)

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Q: Compute Lim メーフ4 7x+5 -3 Sin ? X 2)x-70 3X イメ2+2 3) -00 X-7-00 2x-1

A: (1)Consider the given function with limit:

Q: 14. y" – 4y' = -4te“, Yo = 0, yo = 1 26. y" +2y' + 10y = -6e¬' sin 3t, Yo = 0, yo = 1

A: 14. The given differential equation is, y''-4y'=-4te2twhere y0=0 , y0'=1 Take the Laplace Transform…

Q: If xy tan (10x) + 10 y, then (x-10) y'= Select one: O None O 1/(1+x)+10 O y+ 1/(1+ 100 x ) O-y+ 10/(…

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

Q: 16. tan²(x) + sec²(x) = 1 O True O False

A: Consider a right angled triangle.

Q: 1 Evaluate sin (7/6 + 2e de. 2ei de. 2n Jo

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Q: Prove the following equation : Cosh(3 x) = 4 cosh³(x) – 3cosh(x)

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Q: 1 1. Prove the identity cosh2 r = 1 cosh 2x 2

A: As per our guidelines we are supposed to answer only one question at a time.  Kindly repost other…

Q: 2 сos(6x) — 6 2? — 2 os(6x) – 6 x² sin(5x) – x2 – 5x - | lim x → 0 - -

A: We have to calculate the given limit: limx→02cos6x-6x2-2sin5x-x2-5x

Q: EVALUATE ap- x2 + 64 O x – 8tan + c 8 O none O x – tan -1 +c 8 1 uis2 – a 8 x - -sin +

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Q: Evaluate V1-289z2 sin (16x) + C 17 1 sin 1 (17x) +C 17 sin (16x) + C 17 1. sin (17x) + C 17

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Q: 3 Show that sin"0= 8 2 1 cos (20) + cos (40). 8 Which of the following four statements establishes…

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Q: 2s0ue by usiny Netons method opprozimete 14 sinx+ cosX 1+ sinx- coSX Xis 2.5

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Q: 7. Suppose x is a number such that cos(x) = sin(x). Then: O a) cos(2x) = cos(x) O b) sin(2x) =…

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Q: 1. Assume it is known that cos(x – y) = cos x cos y + sin x sin y for all real numbers x and y.…

A: Solving Q1 Given: cosx-y=cosxcosy+sinxsinycosπ2=0sinπ2=1cos0=1sin0=0sin-π2=-1

Q: 器+7+6= Stn(x + 2y) Sin(x + 2y) %3D

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Q: 4.) Prove: sin 2x a) 2cos? x = tan x b) sin 3x = 3 sin x – 4sin3 x [Hint: sin 3x = sin(2x + x)] -

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Q: If a, b, c, and d are constants such that .2 ax + sin bx + sin cx + sin dx lim 8 %3D 3x2 + 5x + 7x°…

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Q: A) How does 1/2[(1-cosx)/(sinx)+(sinx)/(1-cosx)] equal on of these: secx, cosx, sinx, tanx, cotx,…

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: Prove that X + 8 2 TT sin 8 2 1 sin x X sin?

A: We use Trigonometry identities , double angle formulas to prove this Question

Q: 43. If |2| > 2, then f - dr r = fcos(5) + k B sin-'(5) + k: cosh-" (5) + k: Itanh-"(4)+k B 2

A: by using hyperbolic Trigonometry substitution

Q: у 3 Сі сos 2х + с2 sin 2x y = cqe2* + c2xe²2x

A: See the details solution in below

Q: 28. Evaluate f 5 sin 3x dx 2+cos 3x a. 2 In 15 sin 3x| + C b.- In 12+cos 3x|+C c. In 15 sin 3x| + C…

A: Evaluate integral

Q: Show computations for the other 2 missing values sin 2(-0.001) sin 2(0.001) f(-0.001) = f(0.001) =-…

A: On solving this we will get

Q: Suppose that|x + 4| < 0.024 and |y − 6|< 0.04. Use the triangle inequality to show that |(x + y) −…

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Q: 5. 4 f sin + 2zdz

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Q: 7) 2tan² 0 = 1 + 2tan 0 + 3tan² 0 8) 1= tan² 0 + sec 0

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Q: 4 Giren tan A =– where 0<AS Find 2sin 2A.

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Q: If x(t) = 0.886 +3 cos (5wot) -sin(6wot) , then an , bn a0 5,-1, -6 O 0.886,-1,-6 O 5, -1,6 O…

A: To find the correct option

Q: az az and ду Ql:- Find the if Z = x4 sin x y³. Əx

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Q: Find , if z= cos(3x² + 7y°) O 2x sin(3a? + 7y³) sin(3x² + 7y³) -9x cos(3x2 + 7y°) -6x sin(3x? + 7y°)

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Q: If y= In( 8 tan-1(8x) ) , then y' tan-1(8x) = Select one: O 8/(1+ 64 x² ) O 1/(1+ x² ) O None O…

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Q: 17. If 2 tana tan?ß tan?y + tan a tan-ß + tan B tany + tan?a tan?y 1 (a. B.y e R. a. B.y (2x+1)…

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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: Prove that : A) sin(h3x) =3sin(hx)+4sin(h³ n(n°x) B) 13 cos(hx) 3 C) 2tan(hx) tan(h2x) 1+ tan(h²x)

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Q: 9. y = 3 sin įx 11. y = 4 sin mx 10. y = 2 sin x 12. y = 3 sin 2mx

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Q: Evaluate sin*(2x)dx. sin (2x)dx. sin 4x, sin 8x + C 64 3x 8 8. sin 8x + C 64 O X sin 4x 4 8 8 O 3x +…

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Q: Find the root (7 – 7i)/2 O +7/2[cos(x/4) – isin(x/4)] O +V98[cos(r/8) – isin(x/8)] O +7/2[cos(x/8) +…

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Q: When r^2 = x^2 + y^2, we have x = rcos theta and y = rsin theta, and  When r^2 = y^2 + z^2, we have…

A: Consider the following: When r2=x2+y2 , then x=rcosθ  and y= rsinθ, When r2=y2+z2 , then y=rcosθ and…

Q: y = sqrt ( sin (x^2));y * %3D xcos(x) / (sqrt (sin(x^2)) xcos^2(x) / (sqrt (sin(x^2)) O xcos(x^2) /…

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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.