51. Compute x² _ and then using the identity dx in two ways and verify that the answers agree: first via trigonometric substitution х2 — 1 x +1

Q: 10. Show that 2" + 42' + 8z = 0 if z = e-2=(sin 2x + cos 2x).

A:

Q: 1 Show that L-1{ = (sin hat sin at) s4+4a4, 2a²

A: It is given that, L-1ss4+4a4=12a2sinhat sinat. A partial fraction decomposition of ss4+4a4:…

Q: If +a= a(2 cos 0 cos 20) and y=a(2 sin0 sin 20),show that (z² + y² + 2az) = 4a² (z² + y²). %3D

A: Given that, x+a=a2cosθ-cos2θ⋯⋯1y=a2sinθ-sin2θ⋯⋯2 Squaring both sides of (1) and (2) and adding,…

Q: sec(θ)=11/3

A: Please refer to the image below

Q: 4sin 5x cos 3x-4cos 5x sin 3x/rom x= 0 to x= 2m

A:

Q: 3) Prove that c) cosh2x = 1 + 2 sinh? x

A: In the question we have to prove the given function.

Q: Q3) Ify = in[sec 8 + tan 8) find

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Q: 11. Evaluate the integral: tan 2x dx A. -In| sec 21| + C -sec² 2x + C С. -In| cos 24| + C D. 2 sec…

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Q: find the four non zero terms in the maclaurin serise for sin h-lx

A: Formula Used: We will need following binomial expansion:

Q: Find sin 2x, cos 2x, and tan 2x if tanx= and x terminates in guadrant III. 3

A: To find the value of sin (2 x), cos (2 x), and tan (2 x).

Q: s nip

A: Given z=tanα2

Q: (-1) cos[cosh (In ")]dr 4.

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Q: The integral ¹S. 01-fese csc ³0 de sin² sin ²0 de = [sec³ sec ³0 de + cos² cos²0 de dx (x²+4)² can…

A: We have to solve Integral

Q: Evaluate the following integral. 3 4 4 cos '3x xp. sin 3x 1 18 4 4 cos '3x dx = V1- sin 3x 18 (Type…

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Q: | 6. Use a trigonometric substitution to evaluate x³√x²-4 dx.

A: We will find integral using  trigonometric substitution.

Q: is there a proof that cos^2t +sin^2t=x^2 + y^2 =1 ? if there is , how?

A: To prove the below statement Consider a right angle triangle as shown below

Q: What substitution should be used to solve the integral x²dx |4+9x² O sin u=3x/2 sec u =2x/3 O sec u…

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Q: Q4:B/Simplify [cos 20-i sin2018 [cos 30+ i sin30 1² [cos 40+ i sin40 ]³[cos 20-i sin2015 using De…

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Q: if f(2) = zsin(z) -1 defined on the interval (2. 3] then es using False-Position method equals [x in…

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Q: 5. Find y', if y = 2cosx sin2x – sinx cos2x %3D

A: NOTE:according to company rules I need to solve first question when multiple questions are posted

Q: 1. If z = sin2+In^, find the value of x- +y X

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Q: 5. Find y', if y 2cosx sin2x – sinx cos2x %3D

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Q: (3.2 cos 2x+2 -dx. 1.8 1+ In x Use NINT on the calculator to evaluate:

A: We have to evaluate ∫1.83.2 cos 2x + 21 + ln x dx.

Q: 2 cos(5x) – 5 x² – 2 lim sin(3x) – x² – 3x - - (Write your answer in the given box)

A: We will use L'Hopital rule

Q: 16. If 2 sin 2x s 3 cos2x and 0s 2x then x=

A: Given : if 2sin2x = 3cos2x and 0≤2x≤π2 . then we have to find the value of x.

Q: 1. y = In (3 – 4 cos x) + (4x – 5)5

A: 1). Given function is y=ln3-4cosx+4x-55. To find: dydx Solution: Power rule of differentiation…

Q: e in Q2, find Sin (2e) with 6 If csce -6,

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Q: Show that the equation 2x + cos(x) = 1 has exactly one root. (IVT and Rolle's Theorem)

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Q: 2. Evaluate the integral (cos (3r)sin (3x)dx in two ways, one with u = sin(3x) and the other with u…

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Q: Evaluate the integral. sin (8t + 16) dt cos (8t + 16) sin (8t + 16) dt = cos (8t + 16)

A: Solved below

Q: 1 Find sin 2.x, cos 2x, and tan 2x if and x terminates in guadrant IV. 10 cosx=

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Q: 8 and x terminates in guadrant IV. 15 Find sin 2x, cos 2x, and tan 2x if tanx %3D

A: Given  tanx=-815,  x in quadrant IV

Q: 9-10.j Show that sin20 2tane %3D 1+tan20

A: We will prove the trigonometric formula.

Q: 17. If 4 sin x+3 0 on 0 sx < 211, then x=

A: We have to find x if 4 sin x+3=0 on 0≤x≤2π. Solving the given trigonometric equation, 4 sin x+3=04…

Q: (e²)(sin²2x) Compute In y and In 5z

A: Basic log formula are applied to solve the question.

Q: 35. Use property IV of Appendix A to verify that 1 L'{arctan(a/s)} =sin at

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Q: 5. Evaluate 1. S, sin(x2) dx

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Q: 12. Write an éxpression that gives all sölutions to the equation. COS X - SIn x 3= 2.

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Q: Evaluate the integral / sin 50 do 2+ cos 50 using the substitution u = 2+ cos 50. sin 50 do 2+ cos…

A: Recall: ∫1xdx=ln(x)+C

Q: 5) prove that = sin 'x +e using method of trigonometric substitution.

A: To Prove- Prove that ∫dx1 - x2 = sin-1x + c using method of trigonometric substitution.

Q: The x2-4 dx can only be evaluated using trigonometric substitution technique. A True False

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Q: Determine dy/dx of = 3x(sin(2/2)) O None of the choices O 12/cos (2/2) + sin(2/2) 0-12 sin(22) + 3…

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Q: /2 Evaluate using Wallis' Formula: sin5 x cos6 x dx

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Q: = 2. If y = sin³ (-) cos³ (1) prove that y' = sin² (x) cos(x)

A: Topic = Derivative

Q: Find sin 2x, cos 2x, and tan 2x if sinx= and x terminates in guadrant III. V13

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Q: Show that : |sin x |= CoS nX Σ n2 even 414 2/7

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Q: Find sin 2x, cos 2x, and tan 2x if sinx= and x terminates in guadrant IV. sin 2x %3D cos 2x %3D tan…

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Q: Suppose that 3π/2≤θ≤2π,  csc(θ)=11/4, find sin(θ)=______. (round to 3 decimal places)

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Q: Suppose that π/2≤θ≤π, sin(θ)=2/9, find cos(θ)=______. (round to 3 decimal places)

A: Here, θ is in the second quadrant( π/2≤θ≤π) and cosine is negative in the second quadrant.

Q: 7. Prove that: ++) + sin; + e) = v3cose (3) (a) COS

A: