|(4e + 3z² – 3 sin z)dz =. O 4e² +z – 3 cos z + c O 4e² +z³ – 3 sin z +e O 4ez + 13 + 3 cos z + c O 4ez + x³ + 3 sin z + c O 4e? – 1 +3 cos I +c

Q: (a) cos(iz) = cos(iz) (b) sin(iz) = sin (iz) for all z; if and only if z = nлi (n = 0, +1, +2, ...).

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Q: 9.lf y = sin (4x – 5), then what is y'? O A. y' = - cos (4x – 5) O B. y' = - cos (4x) O c. y' = cos…

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Q: If y = 12y sin(4z) – 12z sin(4y), then (z, y) = 6y? sin(4z) + 3z cos(4y) + h(x) O (z, y) = 6y²…

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Q: pls answer all, thank you

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

Q: The general solution of the DE y"+ y = x is def ined by (y= C¸ cos(x ) + C¸ sin (x) +x 2 (y=C¸ cos…

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Q: Let y = eex + sin(2x), then Y + y' is equal to 2x A 4e2x + 2 sin(2x) (B None of the given choices ©…

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Q: 3(2 + cos t)3 +c Use the appropriate substitution to evaluate the following integrals: . sint (2+…

A: Solution is given as below:

Q: A B O A OB O OD 1 13 (sin(3z))¹⁰ + C 1 33 ſ cos(3z)sin¹⁰(3z) dz 1 3 (cos (3z))¹¹ + C F None of the…

A: Here we have to find the integral.

Q: 12. x²y" – xy + 2y = 0; yı = x cos(In x), y2 = x sin(In x) Je

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Q: won of cos 0) dr + r (sin 6 + cos 0) rsine rcose = C O r + rsine rcose = C 5 + rsine rcose = C r2 +…

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Q: If z = x2 + y² and x t cos 2r and y = r sint, then %3D a2z is at2 (A) 2 cos²(2r) + 2r? cos?(t) – 2ry…

A: Given  z=x2+y2      and x= t cos 2r ,y= r sin t First substitute x,y values in z  Then derivative…

Q: (b) If u = x? cos y+ye», where x= s+2t and y = st, prove that ди 2- ди = (s – 21) (x² sin y – xye" –…

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Q: At what points (x, y) in the plane are the functions in Exercises 31–33 continuous?

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Q: What is the general solution of (sin 0 – = 0 ? 2rcos? 0) dr + rcose (2rsind + 1) do O sin 0 rcos e =…

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Q: If ſ cos* xdx = Ax+B sin 2x+C sin 4x +D, then {4,B,C} equals S3 1 1] 18 32 4 [3 1 1 (b) 8 4 32 ƒ1 1…

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Q: Which of the following is a possible solution to y" +k²y = 0 %3D y = ekz O y = 2 cos kx y = cos k² x…

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Q: S dx √1-x² O-√1-z² sin-¹ z²+z+C O-√1-² sin¹z+z+C O None of the choices O-In 1-2² | sin¹2² +2+C -1…

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Q: Given z(x, y) =In(2xy) where x(u,v)= e" cos(4v) and y(u,v)=e" sin(4v). Find ди 1 cos (4r)+-sin(4v)…

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Q: 4. Evaluate the iterated integral T, cos(³) dydx. a. (cos 1- 1) b. 1 e. (sin 1- 1) f. 1 (1- cos 1)…

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Q: What is the general solution of (r +sin 0 cos 0) dr + r (sin 0 + cos 0) de = 0 ? - rsino rcose = C…

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Q: Find if z = sin(uv)cos(uv), where u = e' and y = e2t. dt %D Lütfen birini seçin: O A. 3e(sin2(e3t) -…

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Q: Q7: Í sin(3z)cos(4z) dz = a)cos z- cos(72) + C b) -tcus x -os(Ix) + C %3D Qe S sin'x cas d = 2).

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Q: 17. (D4 + 2Dz + 1)y = 5 – 3x² a. y = (C1 + C2x) cos x + (C3 + C4) sin x – 3x² + 17 b.y = (C, + Czx)…

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Q: (5e + 4r +4 cos z)dr = O e – r + cos z +c O e +r - 4 sin z +c O 5e + r - 4 sin z +c O 5e* + x +…

A: The given integral is: ∫(5ex+4x3+4cos x)dx

Q: 5. If z = f(x, y), where x = r cos 0 and r sin 0, find z and and hence show that: (). (-(( 2 2 dz dz…

A: To find the partial derivatives of the following function in two variables by chain rule.

Q: dz If 7 = y cos(x), x = s't and y = s²t³, then dt O a) –2s³ ty² sin(x)+ 6s²t²y cos(x) | O b) –2s°…

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Q: 5s Evaluate J|2 sin s Jdtds 0 0 I[ 2 OA. 3 (1 – sin(125)) O B. 3 (1+ sin(125)) (1+ cos(125)) 3 OC. 2…

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Q: 21. a. e x = sec sin z sin z) (e sin b. Ve Cos 2sinz 1 U e sin z COS d. cos x √1-e2sinz

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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: The area of the region inside r = 2+ cos 0 and outside r = 4 – 3 cos 0 is given by | ((2+ cos 0)² –…

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Q: Curves on surfaces Verify that the curve r(t) lies on the given surface. Give the name of the…

A: Definition used-               If curve r(t) lies on the given surface then r(t) should satisfy…

Q: If f(x) = 4c0s(x) , then f'(x) = %3D (A) – sin(x) 4°os(x) (B) – In(4) sin(x) 4cos(x) (C) In(4)…

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Q: is If u = x², v = sin (y) and w = e-3 then the value ofuv.w) a(xyz) %3D ans. -6x. cos(y) e-3=x.…

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Q: Evaluate J J-36z² dz 1 sin (5æ) + C 6. O_ 1 -1 sin (6x) + C O_1 sin (5x) + C 6 -1 1 Osin1 (6x) +C 6.

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Q: x(t) 9 sin (t) A y(1) 4 cos (t) 9 sin² (1) 4 sin? (1) x(1) B y(1) %3D c (1) = 4 + 9 sin (4) DY) = 9…

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Q: Evaluate the integral (@) = / cos (0) + sin(20) – 3 cos(0) sin (0) + 3 cos2(0) + 2 sin(0) COS de 3…

A: Evaluate the integral

Q: 1 SS() di = 2t dt volt do T. |3D -/½ 1 tsin(nt), cos(nTt) (na) 21 cos(nt)dt= 2|tcos(ntt)dt= 2 = 0 n…

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Q: 1. Express as a sum or difference a.) sin 7t sin t b.) cos 6u cos (-4u) c.) cos 2t sin 6t d.) 2…

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Q: • 8 If In = 7/2 e*cos" x dx, where n 2 2, prove that: %3D (a) In = 1-n[" /2 e-* sin x. cos"-1 x dx…

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Q: (a) Prove that dv 1 2 u? + v2 arctan u- + C. 2 u 2, /2/2 ru (b) Prove that I dv du 2 - u? + v2 18 by…

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Q: 3. Jlgu * Solve the D. E. to the I. V. P. sinx(e + 1)x- cosx - 1, y(0) =0 In (1 + cos x) =I+e O…

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Q: 17. (D+ + 2Dz + 1)y = 5– 3x2 a. y = (C, + Czx) cos x + (C3 + C4) sin x – 3x2 + 17 b.y = (C1 + Czx)…

A: As per the company's guidelines we are supposed to solve first question for you, kindly repost other…

Q: L-' (In (s²+25)(s²+16) cos 5t-cos 4i O -2 cos 2t – 2 cos 31 O 2 cos 5t – 2 sin 4t sin 4t-cos 5i t…

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Q: 5)if y =x - 3x* + cos x a) 360x? – 72 + cos x b) 6x5 - 12x3 + sin x c) 120x3-72x + sin x d) 360x2 –…

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Q: J (sin 3x)² = sin 3x xp- sin 3x CO = sin 3x xp- sin 3x On simplifying further, y2 (x) = cq sin 3x /…

A: In this question , constant is to be included in the last solution of the differential equation.…

Q: 2n 1 (cos=0 0 +i sin e) + 10 2cosno eine

A: The general form of a complex number is given by z=a+ib, where a,b are two real numbers and i=-1.…

Q: If z = x2 – y2 and x = t cos 2r and y = r sin t , then a²z is (A) 2 cos?(2r) + 2r² cos²(t) – 2ry sin…

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Q: What is the general solution of sin 0-2rcos²0) dr + rcos0 (2rsind + 1) de = 0 ? %3D O sin 0 rcos²0…

A: Given differential equation is: sinθ−2rcos2θdr+rcosθ2rsinθ+1dθ=0

Q: What is the general solution of (r + sin 0 cos 8) dr + r (sin 0 + cos 0) d0 = 0 ? %3D rsind rcose =…

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Q: (y + 1) dr - (rv +r- 3y-3) dy = 0, when x 5, y = In 4 O y = (x - 3) D y = In (2x - 6) %3D O y = In…

A: Topic :- Differential equation  correct option y=ln(2x-6)