1. [* sin' y cos' ydy 3

Q: 8. Evaluate the integral. sin x xp. 4+ cos x

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: Evaluate sin (44º) + cos (29º) using differentials. Refer to special triangles.

A:

Q: 2.1 Given that sinh x = [e" – e=*] - - show that dy cosh a. da

A: To Determine: show that dydx=cosh x Given: we have sinhx=12ex-e-x Explanation: we have…

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: 28+1 b:If y =-1 prove that. 1- 2y dx

A: # we are entitled to solve one question at a time, please resubmit the other question if you wish to…

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

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Q: Evaluate the integrals in Exercises

A: ∫-ln20cosh2x2dx∫0ln104sinh2x2dx

Q: 4. Evaluate the integral. S tan (2x) sec°(2x) dx

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Q: 7. Show that sin E + x) = G+x): = -cosx.

A: Introduction :

Q: Which of the following is correct? " 17 3 (3 sinh-(x)) = (coth"(x) = (지 < 1) V - 1 dx Option 1…

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Q: In(cos ax) ? limx-0 In(cos bx)

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Q: 3+9sin' x Evaluate dx using suitable technique. cos x

A:

Q: 4. Evaluate 5 cos x dx 3 v2 sin x – 1

A: To evaluate : ∫π6π3 5 cos x32 sin x - 1 dx

Q: 4. Evalaute cos(x) sin(x) dx

A: Given:

Q: 1- d/dz [cosz] = -sin z

A:

Q: establish each identity.

A: Given  The identity is ln sec θ=-ln cos θ

Q: 9. If y = costhen the second derivative is 5x 25 Cos, 16 5x 5x sin- 4 d. 25 5x sin- 4 a. 25 b. C -25…

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Q: 3. Compute 4 (sin? x + cos? x) without using the derivative formulas for sin x and cos x.

A: Given:

Q: dt cos (2 sin 21) /1– 4r

A:

Q: Obtain graphically an approximate value of the lowest root of cos x cosh x =- 1.

A: The equation cosxcoshx=-1 regulates the frequency of vibration of a cantilever. We must first…

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: 7) {(1- sin° 31)- cos3t dt 8) | t in’ (5x)· sec´ (5x) dx

A: 7) I=∫1-sin2 3t·cos 3t dt  ……1

Q: If f(x,y,z)=In(x²y+sin² 12

A:

Q: 1²–1 True or False: cosh (sinh (In æ)) = Select one: O True O False

A: Given: cosh(sinh(lnx))=x2-12x. The objective is to verify the left hand side expression.

Q: (2) If y = (sin-1(x))², prove that (1- x2)y" – xy' - 2 = 0.

A: here first we will derivative with respect to x then squaring both side and put value of the y then…

Q: 3) Show how the substitution u = 2 x shows that - - t/2 -Tt/2 S sin"x dx = S? cos"x dx

A: Let u=π2-x Differentiating u w.r.t. x- dudx=-1du=-dx Considering left hand side of the given…

Q: V3 with 0 < x < 2n. 2 cos 2x cos x – sin 2x sin x - -

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

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

Q: The integral S sine de 1+ cose sec²0 de 1+ tan cose de 1-sine sece tane de sece-1 S x dx x²+√√x²-1-1…

A: dsecθdθ= sec θ.tan θ

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

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Q: 3. In (cose) tane de

A:

Q: 7. Find the derivative with respect to x of tan-(2) – In(2.r +3) = 4 cos (2y +5). %3D

A: To find the derivative of tan-1x2-ln2x+3=4cos32y+5. Solution: Power rule of differentiation states…

Q: EX/ If f (x)= + COS2X CoS X is Pcx) Continlacaus at x=? %3D

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Q: 13 20 Find for Two only of the following: dx 1- y=xtanhx 2- y =cosh 3x- sinh²3x

A: We have to find derivative

Q: Which is the derivative of y= sin In(5x +2)? * 5 cos In(5x + 2) In 5 5Cos In (5x+2) 5x+2 O Option 3…

A:

Q: Show that d 1 In cos(x) os(x) - csc(x) dx 1+ cos(x

A: We have to proof

Q: 4. Evaluate sin (44°) + + COS (29°) using differentials. Refer to special triangles.

A:

Q: 2 2 sin (2t) dt. 8 - cos (2t)

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Q: "+25y 4r sin(51) – 2e" cos(5t)

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Q: In( cosh(11x) - sinh(11x) )= Select one: 01 O 11 sinh(11 x )+ 11 cosh(11 x) O None O zero O-11x O…

A: In this we have evaluate the equation ln(cosh(11x)-sinh(11x)).

Q: 9. Evaluate ſ,(cos x – 1) dx. Tt/2 - π/2

A: topic - definite integral

Q: dy.xandy in =cos = COS e

A:

Q: 3 Differentiate: y = In cosh° (cos 2x)

A: As we know that: The chain rule: fgx'=f'gx·g'x The Power law: ddxxn=nxn-1 From the given problem:…

Q: If we let u = 4x – 1 for theS 2 tan(4x-1)-3 cos² (4x-1) dx, what will be the resulting integrand?…

A: Solving the problem by finding the integrand.