Evaluate. de (sin(5x – 1)] cos(5æ – 1) 5 - sin(5æ – 1) 5 · cos(5æ – 1) • 5· cos(x)

Q: 5. (a) Expand (1+x) and hence find the value of (1.02) correct to 4 decimal place 1+sin 0 m-1 1-sin…

A: First expand 1+x4 then find the value of 1.044 Using the identity, a+b4=a4+4a3b+6a2b2+4ab3+b4…

Q: 1. Which of the following functions are in L¹? in L²? 1 a. sin x |x|3/2 b. (1+x²)-1/2 x²-1 d. 1 -…

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Q: The integral of the given function | cos(9x) cos(5x)dx is equal .. 14 sin 4x + 4 sin 14x А. · + C 12…

A: This question can be solved by applying the formula of 2.cosA.cosB

Q: 4. Prove the following identities: cos? (x) 1+ sin(x) (b) 1 = sin(x) 1- tan (0) (c) 1+ tan?(0) +1 =…

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Q: Prove the following reduction formulas: 1 a) | cos" xdx - cos n-1 x sin x+ cos"-2 xdx

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Q: 2. The limit of the following function equals: x2/3 + x-1 lim x-co x2/3 + cos? x а. 0 b. 1 C. -1 d.…

A: Please refer the attached image for complete solution.

Q: 1) Verify the power reducing formula, cos-x= 0:1 holds true for x = and x= =.

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

Q: 3 Find the exact values of s in the interval [0,2x) that satisfy the given condition cos 2s = л 11т…

A: Topic : trigonometry

Q: sinx S- cos?x+ 6cosx+13 O In cosx+3-Vcos²x+6cosx+13|+C O In cosx+3+/cos²x+6cosx+ 13 O…

A: To find:

Q: 7) y=Flx)=cos" (x) A.) xCcoskl) =4 Cos? (x) %ax (coscx) =4 cas? (x) (-sin(x). 4 Cos (x)Sin(x) %3D…

A: Explanation of the answer is as follows

Q: R4 for g(x) = cos(xx) on [0, 1]

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Q: 2. : (a) For n ≥ 1, show that 1+z+2²+...+ 2¹: (b) Hence, show that 1+ cos 0 + cos 20 + 12+1 2 #1 7…

A: Solution:

Q: 3. Find g'(x) if g(x) = sin³(4x) %3D A. cos (4x) B. 3 sin?(4x) cos(4x) c. 12 sin (4x) cos(4x) D. 4…

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Q: Find all values of x between 0 and 2pie that satisfy the quation.   cos x = -1/2

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Q: 6. Let z1 = x1 and z2 = x2, with x1, X2 real, and the relationship ei(x1+*2) = etx1ętx2 to deduce…

A: A detailed solution is given below

Q: 2 Find the maximum and minimum values for f(x) = . Determine the -4 + cos x+ V3 sin x angles at…

A: Consider the  given function fx=2-4+cos x+3  sin x The value of the function at the endpoints of the…

Q: 11) (3ysos(3a By cos(3

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Q: 1) VERIFY THE POWER REDUCING FORMULA, cos"x : cos 2x+1 HOLDS TRUE FOR 2 x = - AND x =

A: To verify:   cos2x=cos2x+12, for x=π3 and x=π2   NOTE: As per our answering guidelines, we can only…

Q: 4) Find the value of cos(1.74) from the following table oot x y = sin(x) Hint: dy dx 1.7 0.9916…

A: The given problem is to find the value of cos(1.74) by using newton divided difference method from…

Q: 1 1 1 cos a + cos 3a Cos a + cos 5a 1 Cos a + cos 7a +.... + cos a + cos(2n + 1)a 1 cosecaftan(n +…

A: Given that, We have to prove that, Consider the nth term of the left-hand side, By using the…

Q: 2. Prove each of the following using identities, showing all work in the process. a. cos(x + ) +…

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Q: e) cos (x + y) - cos(x - y) =-2sinxsiny

A: Given that, cosx+y-cosx-y=-2sinxsiny. Note that, the formula for cosA+B=cosAcosB-sinAsinB and…

Q: 2 72 Given n is a positive integer, (V3 + j)" + (V3 - j)" is 2n+1 sin O () 2" cos 2" sin (") 2n+1…

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Q: 2n3+n² sin(n)+6 48. Calculate lim,,→0 312 cos(m10n 19: (Proof is not required)

A: Use the algebra of limits to find the limit of the given fraction, and use a concept that limit of…

Q: f (0. 80108) = sin 3 (0. 80108) + cos 2 (0. 80108) – (0. 80108)²

A: Given,

Q: (급-) 금- 1 2 lim 1-x 1-a2 a. x 1 lim x→1(1 1- x- 21- x 2) 2 cos? x+3 cos x-2 lim xT/3 2 cos x-1 (This…

A: we have to find limit

Q: Which of the following function is harmonic in the C- (0}: COS Z Re (- COS Z Im (

A: To find the harmonic functions out of all the functions.

Q: 2.Expand the following in powers of x i)√(1 + sinx) ii)e cosx iii) cos x²+

A: Given data:- (i); 1+sinx (ii); excosx (iii); cos-1x2-1x2+1

Q: (1) List the first 5 terms of oach of the soquence (a,). n+1 (d) an = sin An = 3n- - 1 3(-1)" (e) a…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: (1) Evaluate the following functions 1. In(3-i6) 3. cos (1+i3) , 2. e(0 52) , 4. tanh (2-i5)

A: As per guidelines, we solve only first question. 1. Given      ln3-i6

Q: 3 sin x If f(x) then 1+ cos x f'(x) = f'(1) =

A: topic -derivative of a function

Q: (-1)"x2" Σ (2n)! 1. For all x E R, cos x = n=0 +00 (-16)"(4n+1) (2n)! c. Use the result in item 1(b)…

A: We have to prove the sum of series.

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: 1. Perform the indicted operations (2D² – 3D + 5)(x cos x – 3)

A:

Q: 1. Determine the absolute extrema of f(x) = (sin x – 1) cos x on 2' 2 if they exist, and identify…

A: Given:-f(x)=sinx-1cosx,        x∈-π2, π2f'(x)=sinx-1ddxcosx+cosxddxsinx-1…

Q: 1. For non-negative integers n, let k +1 k +2 Σsin n +2 n sin k = 0 n +2 f(n) = Lsin-( k +1, k = 0 n…

A: Given f(n)=∑k=0nsink+1n+2πsink+2n+2π∑k=0nsin2k+1n+2π

Q: 2. Find g'(x) for g(x) = x cos-l-V1- r²+ez³ cos z. [Simplify answer as much as possible.]

A: topic -derivative

Q: -1 -1 18. Show that cos (-x) =T- cos x

A: We have to prove that cos-1(-x) = π - cos-1x

Q: Given x[n] = x1[n] + x2[n] where, Ttn x1 [n] = 9 cos and x2[n] = 8 sin 4 8

A: Given: xn=x1n+x2n x1n=9cosnπ4 x2n=8sinnπ8 To do: Graph x1n using Scilab.

Q: 1 Evaluate Le' cos 2t +÷sinh 2t

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Q: Consider the image attached of the functions f(x) = 12*cos(2x+1)-6 and g(x) = -1. Set f(x) = g(x)…

A: Given that, the functions are fx=12cos2x+1-6 and gx=-1. Equate the functions to find the solution x…

Q: 1. Determine the absolute extrema of f(z) = (sin a – 1) cos z on -. 2 if they exist, and identify…

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Q: 2. Prove each of the following using identities, showing all work in the process. a. cos (x +) +sin…

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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: -1 -2<x< - 1 0 -1<x<1 1<x<2 nswer: f(x) = a + Tin COS ... COS n=1 sin T²n² O sin () COS

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Q: -ツ() The function f(x) is invertible. Find given that f(x) = 5x +4 cos(x).

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Q: 8. Find all values of 0, if 0 is in the interval [0°, 360°) and cos 0 V3 2

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Q: Q2) 1- Find O for: y= cos (x) + cos(x)

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Q: 3. Prove there is at least one x E R such that e* 2 cos x +1

A: We have to show there exist x€R such that e^x=2cosx+1...... (I)  We plot the graph of both function…