If A =x 2sinyi+z?cosyj -xy2k then -=x?cosyi - z?cosyj-2xyk 1O ду =x?cosyi-z2sinyj-y?k ду .II O =x?cosyi -z?sinyj -2xyk O ду

Q: evaluate the integrals

A: since you have posted multiple questions , so I'll solve first one for you, for rest question's…

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

A:

Q: 2. Find an interval where f,(x) = sin2 x and f2(x) = cos² x are linearly independent. %3D

A: W(π/4) = -sin(π/2) = -1 W(π/6) = -sin(π/3) = - √3/2 Since, Wronskian is not zero for a single value…

Q: V. Show that: 1. [(cosx-sin x)'dx = x+ cos 2x +C 2.

A:

Q: Differentiate: y = sinh° (sin 5x) Oy' = 15 cos 5x sinh (sin 5x) cosh(sin 5x) Oy' = –15 sin 5x sinh?…

A: dsinh (ax)dx=a cosh (ax) dsin(ax)dx=a.cos(ax)

Q: find the volume of the solid

A: Find volume of solid.Sketch the given function.

Q: Find where z = sin (x²) cos (y) COS © 6.x sin (x²) cos (y²) COS 2.x sin (2²) 2x cos 2.x sin (x²) cos…

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

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Q: 4. Find fyryzyaz, if f(r, y) = x² cos[100(e" + /1+ y²)®]

A: Given; f(x,y) = x2cos[100(ey+√(1+y2))y]

Q: Find the general solution of y'=cos²xcosy

A:

Q: sin (2t + 1) - dt cos? (2t + 1) 31.

A: Use trigonometric substitution method for solving the integral.

Q: The integration expression + 4)cos(3ln(x) +4)dx must be transformed into using suitable choice of…

A:

Q: Prove Sinhu.sinhv=1/2 (cosh (u+v)-cosh (u-v))

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Q: + Bsin z Differentiate @ wi th xespect to x - - S"d (use dy A sinz + B cose

A: Given that: y=Acosx+Bsinx

Q: Find dx ar and simplify the result whenever possible *+ sin2x sin' 5x 1. y = 2. y sin5x 3. y sin? 4x…

A: Given  The equation is y=-35cot5x3+cot3x3-3cotx3-x

Q: „In sec²(sin2y)dy can be evaluated by writing it as sec2y A sec²(sin2y) - cos2ydy None © In…

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Q: z = 2ev Ве ev-sinx – 3e*÷cosv) find: www a2z a2z az a)- дудх ,b). дхду 4 ax

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Q: Compute[x² sin(2x)dx. A.- x² cos(2x)+ xsin(2x)+ cos(2x)+C 1 1 B. — — x² cos(2x)+ —…

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Q: 3. Show that sinh a + sinh y = 2 sinh cosh %3D

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Q: 2 Find def differentiêt equatcn of: -I(082 Siny %3D

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Q: Use Fourier cosine transform to solve y" – y = 3e-4 y' (0) = 0 lim y (x) = 0, as x → o0

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Q: zy (Smxa CosX) Axー Sinhy

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Q: 24. Evaluate: S(cos 2x) esin 2x dx A. -e sinzx + C esinzx +C C. esinzx + C esinzx D. + C В.…

A: using substitution method to solve integration

Q: 3. Prove that coshx – coshy = 2sinh () sinh ().

A: As per honor code we are entitled to solve only 1 question at a time so I am providing you the same.…

Q: sinh (u+v)=sinhycoshr+ coshuxsinhv

A: Use hyperbolic function

Q: Q1: show that 1) d/dz [cosz] = -sin z, * 2) 1+tan2 z = sec2 z

A: 1) ddz(cos z)=-sinz2) 1+tan2z=sec2z Results:ddxf(x)=limh→0f(x+h)-f(x)hlimx→0sinxx=1limx→01-cosxx=0

Q: Step by step

A:

Q: Differentiate y= cos y2x +1 sin 2x+1 A. V2x+1 sin 2x+1 B. V2x+1 sin 2x+1 C. V2x-1 sin 2x-1 D. V2x+1

A: Please refer the attached image for complete solution. THANK YOU.

Q: 3. Solve the IVP: siny(x + siny)+2x²cosy y'=0; y(-1)= π/2 (Subst. first and then Bernoulli's)

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Q: Find dy if y= 5x² sin4x dr O None -20x? cos4x – 10xsin4x 20x² cos4x + 10xsin4x O 10x² cos4x +…

A: We apply u*v rule of derivatives d/dx (u*v) = v*du/dx + u *dv/dx

Q: Find Fourier transfarm f x #1= cos aut ut

A: Given the x(t)

Q: Find y' where y = 8 cos-1 (sin (19 z)) – cot-1 (14 z) Answer: 14 y' = -152 1+196 z2 -152 cos(19 z) +…

A: This question belongs to derivative of inverse trigonometric function.

Q: ♥ дzu ахбу = сезх созу, Ans: u(x,y) = sinx siny + x² + 2 cosy - #2² X 1 бу исx;#) =X бx U(x,п) =X,…

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Q: Show that coshr+ sinh a = e and cosh r- sinhr = e. Hence, deduce UTMOU cosh r- sinh z = 1.

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Q: Find and simplify the result whenever possible dx 1. y=x+sin2x 1. y = 4 1 sin' 5x 3 2. y sin5x - 3.…

A: Solving for the number 4:                                          4) y=3xcos(x3)-9 sin(x3)   To…

Q: Show that y1(t) = cos(3t) and y2(t) = sin(3t) are linearly independent for all t

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Q: Integr S√₂-cod -1 ation fuctions. 1-cos²x) dx Not of the above B 1 O

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Q: 4) z = (4 + j3)sinh(3+j)+cos(3-j2)

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Q: Differentiate D = x2 + sin25x with respect to t and simplify. x2 + sin? 5x dt dt x2 + sin2 5x)1/2 dt…

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Q: find do diy y = (cos(x))*os)

A: Given y=(cos(x))^(cosx) Now differentiate y with respect to x

Q: az Use an appropriate form of the chain rule to find dt 1 z = 2 cos x sin xy; y = 5t t Enter the…

A: z=2 cos x-sin xy ; x=1t; y=5t   see z is a function of x and y ,where x and y are functions of t so…

Q: Use Cramer's rule to solve for x' and y' in terms of x and y. x = x' cos 0 – y' sin 0 y = x' sin 0 +…

A: Solution is given as below:

Q: if t(い) = ta Cosy V = X siny Determine JR ļ JR to つメ

A:

Q: if we let u-4x- 1 for the 2 tan(4x-1)-3 cos (4r-1) dx, what will be the resulting integrand? cos…

A: The given integral is  (2tan(4x-1)-3cos2(4x-1))/cos(4x-1).

Q: a3z cos(x – 4y) show that a3z 6. For z = дудхду

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Q: 11 csc²(3x) cot(3x) dx =, (Use Substitution Method) 11 11 +C 6 sin (3z) 6 11 11 +C 6 sin (3z) 6 11…

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Q: Find the solution. 7. (3siny – 5x)dx + 2x2cotydy = 0 hint: let z = siny

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Q: 26 csc (2x) cot(2x) dx (Use Substitution Method) 26 26 + C 4 sin (2x) 4 2 26 26 + C 4 sin? (2æ) 4 26…

A: Integration.

Q: 6. Vsin x sin 2xdx Vtan 4x 7. J cos² 4x 8. cos 2xsin 2.xdx |arctan(3 – x) - dx 9. 1+ (3-х)? 3e 2y…

A: Given

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.