c) 2cos?x + sin ( +x) – 1 = 0, ja 0 < x < 2n

Q: | 12sin z cos zý3 sin? z + e® dz

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Q: If x = t + 2 sin(at), y = 3t – cos(nt), evaluate at t =;

A: Given that x=t+2sinπt, y=3t-cosπt, we have to find dydx at t=12. Now, dydx=dydtdxdt…

Q: 3. What we want to do next is write (x + jy)as Relº where R = (x2 + y² ) and tan-1(0) = (2)

A: If you have a complex number z = r(cos(θ) + i sin(θ)) written in polar form, you can use Euler's…

Q: 6. Y 12 12 9. 15 15 X. sin (Z) cos(Z) %3D tan(Z)

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Q: Compute -i + cos -i sin a - sin a + i cos a where a E (T, ).

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Q: Q2. C{sin 2t} L{ (a) (c) (b) π π – tan KIN K FIN FIN (d) - tan-¹ s = tan-1 SINSINSK tan -18 2 -1 2

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Q: d Q 3. Prove that tanx dx sec?x. =

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Q: S cos“ xdx = sinxcos² x + sinæ + c Select one: O True O False

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Q: cosh? z + sinh2z=1 true False O оо

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Q: Q: If cosece - sin e = t and sece - cos e = m, prove that l'm? (12 + m2 +3) =1 1. %3D

A: Given that cosecθ−sinθ=lsecθ−cosθ=m

Q: 5. Demonstrate the following identity: Ecosnt : cosme sin (m+1)0 sin n=0

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Q: Suppose sin u=x and u is between 0 and 2. What is cos u? V1-x2 | VI- 2² 1

A: Consider the following equation: sinu=x Consider the following trigonometric identity:…

Q: The length of the curve y= In(cosx) between X=0 and X = TT/3 is given by: a. None of the other…

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Q: If u = tan -1 x- the value of x2 +y?+xy du at x = 1 and y = 3 is

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Q: 8 Find the anti denivapine Sfa) faa or © f la) = Cos ( 6x) 16 - Sin? ( 6x)

A: f(x) = cos(6x)16-sin2(6x) ⇒I=∫f(x) = ∫cos(6x)16-sin2(6x)dx Since dsinxdx=cosx, therefore:…

Q: b) Describe, the motion of a particle with position (x,y) as t varies in' tthe given interval X= 5+…

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Q: 6. If f(x, y, z) = r³y³ sin (z²)+z³ cos (r³), find an expression for fryz and evaluate it at the…

A: x, y and z are the variables of function f Differentiating partially the function f with respect a…

Q: where yco,t) = y (5,t) = = 2Jx2 and y cx, o) y (X,o) = 10 sin 4T X

A: We solve the differential equation by the method of saperation of variable. In this method we…

Q: The cos'ydy is equal to 3 A. siny + sin?y +sin³y - sin'y+ C sin'y + C 3 1 B. siny – sin³y + siny -;…

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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: only 8 please

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Q: /4 sec? Vwdw a) b) sin 2.xcos xdx c) f tanh xdx

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Q: Defnie x Sin ( fG.9) = %3D %3D is corfinugs al Co,0)

A: *** This is the problem related to Multivariate Calculus and we are advanced math expert and have…

Q: a2z a2z dz Q3) A: If e-(sinx + cosy), show that ax2 ду? at

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Q: tan? z sec? x + sec a Prove 1-cos I

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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: Given y = cos(3x), find O O 3 2- * N O √3 3√3 dy at x = 5

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

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Q: 7. Let f(x,y)= a) T 2 xsin y-y, find sin x+y Simplify and give exact value

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: Q9: If F(x, y, 2) = [sinh-(sin- (In (/sin(cos(x²)) y? + zyx + y, find and ду az Q10: If z =…

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Q: At which of these x-values is the value of y=cos x greater than the value of y=sin x? Select all…

A: From above we can see that when x=π6, (cos x,sin x)=32,12 here cos x&gt; sin x From above we can see…

Q: 7. 10 Integrate the given belo trigonometric substitution by dx S Vix?+2x) O x +1 = sin 0 O x = sec…

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Q: What are the values of and cz so that y(x) = cq sin(x) + c,cos(x) will satisfy the conditions y(0)…

A: Given y (x) = c1 cos(x) + c2 sin(x)and y(0) = 1,   y'(π) = 1

Q: Given that r = 3 cos nt, y = 3 sin at and z 4nt with 0<t <1. Evaluate (x+ 2) ds.

A: The line integral is defined as,

Q: 1) If dy = tan x, then y =? dx А. !tan?x + C B. sec?x + C C. In [sec x]+ C D. Inſcos x] + C 2) dx =?…

A: We have to choose the correct option.

Q: Given that (-) x sin-1 -1 = COS eya. dy in the terms of x and y. dx Find

A: Given: xsin−1⁡1y=cos−1⁡eyx Since, dsin-1xdx=11-x2 and dcos-1xdx=-11-x2

Q: 22. Determine Sz sin? y cos y dy

A: Given that: ∫0π2sin2ycos6ydy

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

A: We have to simplify

Q: Q2:- Find fo, fe , fo if f(p, 0,¤) = p² cos ¢ sin 0. cos O sin 0

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Q: In Va? + b² dx In x arc tan- Jo (x + a)² + b² where a and b are real.

A: We will prove the given identity by solving the integral using appropriate substitution.

Q: 0, o° s 0 < 360°, given the follo Cos e = and 0 in QIII 2.

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Q: Which of the following is correct? 1. cosh²x + sinh²x = 1. II. sinh x cosh y = sinh (x + y) + sinh…

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Q: ja o <x < 360 b) sin (2x +) = 0, ja -n<x< * a) cosx = c) 2cos"x + sin (+x)-1=0,ja 0 <x< 2n

A: For (a),     cosx=-32⇒x=5π6+2πn, x=7π6+2πnFor 0≤x≤2π,⇒x=5π6, 7π6

Q: I sin(z) cos(z) da : Hint:

A: Given integration is, ∫xsin(x)cos(x)dx We know that, 2sin(x)cos(x)=sin(2x) Now, the integration…

Q: 3) Show that y" +y = 0, given that y = 2 sin x + 3 cosx

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Q: your answer in terms of both x and y. (a) x2 - ry + y? = 5 (b) cos(x + y) = x² 1 (c) -- - = 4

A: Use implicit differentiation to find dy/dx

Q: Evaluate. S cos z In(sec z)dz Your Answer: In(sec z) sin - In tan z + sec + sin z + C

A: Please see the answer below.

Q: (a) Evaluate O ezz C cos(TZ) where c is z = 1

A: The objective is to evaluate ∮Cez2cosπz where C is z=1 Singularity of ez2cosπz are,…

Q: /hich of the following statements is true? +C (x-5) In(3) B dr=sec-!(x) +C tan²(x) dr =tan(x) – x +…

A: We are going to solve

Q: Find the convolution of fix) = sin bx, g(x) = exp(-alx), a>0.

A: Convolution: Let and be two piecewise functions, then the convolution of them is denoted and defined…