) Solve Hhe following equation for X in [o,27) 2 Sin x -Sin t-1=0

Q: 4. Prove that the equation x + sin(x) = 1 has at least one solution in the interval |3D Va + 3 (0,…

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Q: need help with attached, thanks

A: Given function and interval are,

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Q: Find 7'(t), given ř(t) = ( – 4cos( – 5t), 3 sin( – 5t), e*). - - F (t) =

A: Solve the following

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A: To evaluate the given definite integrals.

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Q: a) Show that U = e-x sin (nt) is a solution to a²u = 0. %3D ax2 at2

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Q: Find the length of the curve. cos(4t) i + sin(4t)j + 4 In(cos(t)) k, 0 <t< n/4

A: We have to find the length of curve.

Q: 5. In AABC, m2B = 90°. sin A = 2x + 1.5 and cos C = 3x – 0.9. Find x.

A: Given: In Triangle ABC∠B=90οsinA=2x+1.5cosC=3x−0.9x=?

Q: -3+ Sin zt dt 7 8-1 i uct-1) } e-zt 9- to

A: As per our guidelines I am solving only 1st for others kindly resubmit the question mentioning that…

Q: 2.) If H (y) = cos y – sin y, find H (0), H (n),H (T), and also show that H. n+ x) = H (n - x) = -H…

A: The solution is given as

Q: A-Show that S 1, L{cos at} s2+a²

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

Q: Prove that x2 cos x dx = T(2 – n) (+ sin æ)?

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Q: If u(t) = (sin(4t), cos(2t), t) and v(t) = (t, cos(2t), sin(4t)), use Formula 4 of this theorem to…

A: Find u(t) . v(t) first then differentiate with respect to “t”.

Q: Let z = 8(cos 50° + i sin 50°) and w=2(cos 30° + i sin 30°). Express in the form r(cos+ i sin 0):…

A: Here we can use the following formula to find the results eiθ=cos θ+i sinθande-iθ=cos θ-i sinθ

Q: 18 a Show that / (1 + sin 2zx)dx = n, for all positive integers n. b Sketch y = 1 + sin 27x, and…

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Q: 5. Let y (sin(2r)) (nz). Find 2. Express your answer only in terms of r.

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Q: 10. Prove that T/2 75/2. sin e cos (cos a cosec 0) de 10 T 2 (1-cos a).

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Q: Find / sin(2r) PV -dr R I +4 by invoking Jordan's lemma.

A: Sol

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Q: Determine c1 and c2 so that y(x) = c1 sin 2x + c2 cos 2x + 1will satisfy the conditions y(?/8)= 0…

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Q: Show that 0 π/2 st sin? xdx TT/2 [ 0 cos? rdr 2

A: A detailed solution is given below.

Q: 4. a. Show that for 0 Va² + sin² a. b. Generalize the result in part (a).

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Q: (a) , f(r cos 0,r sin 0 )rdrde

A: Answer and explanation is given below

Q: Find 7'(t), given 7(t) - 4e 2t (3 sin(2t), ,4 cos(4t)). F'(t) =

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Q: The value of f(z) = e² at z = 3 + 4i in terms of x + iy is O a. 1 O b. e cos 4+ie sin 4 O c. e*…

A: Given, We have to find the value of  fz = ez  at  z = 3+4i  in terms of  x+iy  .

Q: 18.) Suppose x = R cos(0) sin($), y = R sin(0) sin($) and z = x² + y? + z? = R²Y R cos(). Verify the…

A: Given

Q: əz Əz Əx Əy Q5-A) If z =(x +by)² +e+by+sin( ax +by) show that b =a

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Q: T/2 TT/6 sin x 2 1.)Prove that

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Q: If f(1, y) = e“ sin 7y, then fay is given by: o - 28 et sin 7y O - 28 e“ cos 7y O 28 e" sin 7y O 28…

A: Given that: f(x,y)=e4x.sin7y

Q: 41 cos t dt = 1+ sin?t /2 If q sec e de, then a = b = and q =

A: Solve the integral in the following way:-

Q: 7/2 79. Prove that 0< sin x dx < Ja/4

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Q: du Given u In[y cos(3x²y)1, solve CoS %3D ax

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Q: (Q6) Solve the following non-linear algebraic equations: (a) 2ex + sin 2y + 22 5, sinhx + 22+1 2sin…

A: Since you have asked multiple questions, we will solve first question for you. For other question,…

Q: 1. If Z = sin r+ 2 I+1 6. - ", find dZ/dr.

A: differentiate with respect to x

Q: 1) Solve det [i4(îĥ.ở)] where ở li ). and în = COS + sin j. (i = V-1)

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Q: 1.Why does the following DE have an unique solution on an open rectangle that contains the point (O;…

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Q: Find the length of the curve over the given interval. =8 r = 7(1+ cos 0), 0 <0< 2n

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Q: 7 (a² +b°) 1 Prove that : dx = ở (a sin x+ b° cos² x)' 4a’b?

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Q: (2{co(;)+ sin(;)})" Simpli fy, z = 1+v3i 0 22품 0 22플 O 42 O 24-

A: We have to simplify

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A: Given: ∫0π2cost4-sin2tdt Let sint=xcost=dx Then sin0=0sinπ2=1 So, ∫0π2cost4-sin2tdt=∫01dx4-x2

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Q: 4 sin 2t + 2 tan 2t = 0 %3D

A: 4sin2t+2tan2t=0

Q: Solve the equa tion on the interval [ o, 2 ) 2 sin? 9-3 sin O +1 =0 tan2x-1 =0 (2 cos x +JE) (2 sin…

A: As per bartleby guidelines we only give first three question answers.

Q: .2π π 1 -εrocos? θ r dr sinθdθ φdφ x 32 πο X = ?

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Q: Determine cı and c2 so that y(x) = c1 sin 2x + c2 cos 2x + 1 will satisfy the conditions y () = 0…

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Q: For how many a E (0, 1) will sin(x) + a sec(x) = cos(x) + a csc(x) have at least two distinct…

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Q: If r(t) = (VE – 1, ln(10 – t), sin(2t)) then the domain of r is

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Q: 22-j is 1. -1+jZ If Z = cos 0 + j(1+ sin 0), show that the magnitude of

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Q: Show that, for any constants k' and 'a', u = sin(kx) sin(akt) is a solution of the equation Ut =…

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