3n + cos² . + 2n Prove that Limit + cos²P 2n cos²P p + r + cos?P 2 2n ...... 4r f= 1

Q: Prove that 1-x ', V 2 1+x cos'x = 2 sin 2cos 2 COS 1 -1

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Q: ve that Limit n + cos² . 2n cos + cos²P. p + r + cos?P. +...... 2n 2n f=1 4r

A: Given limn→∝ 1ncos2pπ2π+cos2π2n+....+cos2pnπ2n=limn→∝1n ∑r=1ncos2prπ2ntaking n=1nthen takling…

Q: 1 Bin x į sin x, 0sxsn, Prove that f (x) = + 2 2 · If f (x) = { 0. cos 2nx -- n=1 4n? - 1 1 Hence…

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Q: The area of the region inside r = 2+ cos 0 and outside r= 4- 3 cos 0 is given by T(2 + cos 0)? – (4…

A: We will find out the required area of the bounded region.

Q: (a) Show that z" + z=" = 2 cosn0. (b) Hence show that 32 cos5 0 = A cos 50 + B cos 30 + C cos 0…

A: Given:- Let z= cosθ+ i sinθ

Q: Prove that V1+ cos x +VI-cos x X +÷,0<x<. 4 TT - 1+ cos x -V1- cos x 2 2

A: PS: There seems to be a cut in the image. If this is the question, pls find below its solution.

Q: In 4 4. Co CoS X メ→0

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Q: #/2 |cos" xdx kn/2 If 0 then K = %3D

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Q: Show that |cos x - 1| &lt;=|x| for all x-values. (Hint: Consider ƒ(t) = cos t on [0, x4].)

A: Mean value theorem states that

Q: Let C be the shortest path that connects a to zi and I = f. (sinhz + 1)dz. Then None of these…

A: Second option is correct answer i. e.  I= -1-cosh(π)+π(i-1) . Thankyou !

Q: @) 2) Fs of (x) = -PFC (Psy) -} [ If f (x,y) → as 6004X proof. (H-w.) then в

A: Introduction: The Fourier sine and cosine transforms are variations of the Fourier rework that do…

Q: Let C be the shortest path that connects n to ni and I = S. (sinhz + 1)dz. Then Ι-1-cosh π+ π(-1)…

A: For the first question . Option first is correct answer . Thankyou !

Q: 2 Prove that lim x*cos 0.

A: Explanation: Given that,  limx→0x4cos2x=0     Taking LHS(Left Hand Side) limx→0x4cos2x

Q: Which of the following is true? cos(x) + cos(7x) A Scos(3x)cos(4x)dx = J 2 J sin(4x)cos(3x)dx = […

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Q: 4. Show that f(x) = sin(x² + 3x) is equal to g(x) = -x cos(x) at least once on %3D Hint: Think about…

A: Given that, f(x) =sin(x3+3x),  g(x) =-xcos(x) Given an interval as -π,-π6 To show that f(x) and g(x)…

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: du azu Find the solution to the equation = k at ax2 satisfying the conditions 1 - ax 0 at x = 0 for…

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Q: 2c. Show that * (5 - ) 4 sin z - cos 2r + 3 -8 cos for every r.

A: To prove: 4sinx-cos2x+3 = 8cos4π4-x2 We know that cosx-y  = cosxcosy+sinxsiny and cos2x= 1-2sin2x

Q: 9 If f(0) = cos 0, cos 02 cos 03 ..... cos 0n %3D Show, {tan 0, + tan 02 + tan 03 + ......... + tan…

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Q: a) By using convolution theorem, show that 1 (sin 3t – 3t cos 3t). 54 1 L-1 (s² + 9)2

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Q: The limit in lim (46 x; - 28 sin (x;)) Ax i=1 on the interval o, is equal to 2 (23 x² + 28 cos (x))…

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Q: 5. Show that cos x = x has a solution in the interval [0, 1]. Hint chow that f (x) = x cos x has a…

A: Given, Cosx =x

Q: Taking Joint H. Ź Fx=0 FHo Cos 45- Fan Cos67.5 Ho +130-6 563 cOszas:0 67.5 45° :: FHo Cos 45-Fan…

A: A system of equation is a set of equation with common variables in them. The solution of such an…

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

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Q: 6xsec 3x 2-If y = (tan3x)" prove that = (tan3x)²"| + 2ln(tan3x) %3D %3! tan3x

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Q: Prove the reduction formula: cos" xdx : 1 -cos"- 1-1 x+ cos"-2 xdx %3D -

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Q: Theory and Examples

A: limx→02x23-3cos x

Q: converges, then C„-)" " con COr n=0

A: We have to choose the correct answer from the given option according to the given series

Q: C 3y° cos xydydx = O 3(1-Cos3) 5(1-cos3) cos3-1 O 5(1-Cos3)

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Q: v3 V3 sin 30 = , cos 30° = , tan 30° = COS %3D O sin 30° = , cos 30° = . , tan 30° = %3D %3D V3, cos…

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Q: Find the root (3 – 3i)2 - + V18[cos(r/8) + isin(x/8)] O +V18[cos(x/8) – isin(t/8)] +3 V2[cos(1/4) –…

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Q: The limit lim (18 x; - 28 sin (x;)) Ax i=1 on the interval 0, is equal Tt/4 | (9 x² + 28 cos (x)) dx…

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Q: x=cos¬! 1 prove that sec" X= cos

A: Given sec-1x=cos-11x

Q: 2k2 sin(k/n) lim is n3 k-1 1. cos(1) + 5/3. 2. cos(1) + 1/3. 3. cos(1) + 2/3 4. cos(1) – 1/3.

A: We have to solve

Q: 3. Show f cos2n Ode 277 sin-n Ꮎ ᏧᎾ = 27 22n 11.1 n = 1, 2, 3,...

A: Using Cauchy integral formula.

Q: n x)(\sec x+\tan x) \equiv \cos x, \quad nathbb{Z} .

A: (a)  To prove that: (1-sinx)secx+tanx≡cosx

Q: 7.2 (A) 1. S sin x dx cos x + C because(-cos x +C) = %3D dx 2. S cos x dx = because sin x 3. S tan x…

A: We need to solve the given integral. This can be done as follows:

Q: 2k sin(k/n), 212 lim is A-1 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: a3z cos(x – 4y) show that a3z 6. For z = дудхду

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Q: tan 4X Prove that 4t(1-ビ) if 1-6t +tf t=tan

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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: [6z" cos(2) dz =- O 6 r* sin(x) – 18 z² cos(x) – 36 z sin(z) – 36 cos(z) + C O 6z° sin(z) + 18 z²…

A: Explanation of the solution is given below...

Q: derrivative of: Cos(xy)+secy=5

A: Consider the given expression as cosxy+secy=5

Q: 16. So the maximum occurs at an angle of 0, but only if the angle is small enough. Explain why that…

A: Given: v=2μgscosθ+μsinθ Here μ is the coefficient of friction, g is the acceleration due to gravity…

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: lim (1 - cos(3x))sin(7x) of (c) 이이 O 0° O 100 O o. c0 O co - c0 O not indeterminate 8 %

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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: 3: Solve ODE Cist Order a. dY

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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.