er +6 近 。 Oe) sin(2a) Od) cos(2x) T SOƆ 7 5 Ob cos(x²) + 2x (,r)so) (e O ap UIS .2 hip If y = sin(x²),

Q: 7- y" + 4y = cos x, y (0) = 0, y(n) = 0

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Q: 1. S sin’y (2 – 3 cos y)°dy

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Q: (s,+)=(-3,1) X=5?+2+? y= 6st a) 4s x sinly) + 6+x?coscy) at (-3,1) b.) 8tx Sincy) + 6sx? Coscy> at…

A: GIVEN  (s,t)=(-3,1) X=s2+2t2  Y=6st substituting the value of s,t for X and Y we have  X=(-3)2…

Q: z = 2e"žsinx – 3e*cos(y) Ве find: www a²z a2z (n az а) дхду"") дудх ,b) ду

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Q: = 0 If 2 sin x cos x + V2 cos x = 0. 0, then %3D %3D or

A: 2sin x cos x +2cos x=0

Q: 5. y = tan- (a) 6. y = 4x sin (3x - 9) 7. y = sinh (4x – 1)

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Q: cos 2x he ƒ -dx is 4+sin 2x {A} In|4 + sin 2x| + C {B} In|4 + sin 2x| + C {C}(4+sin 2x)² + C {D} -(4…

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Q: So 3 3 cos y sin y dy

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Q: Q. It sin x Cos X XCOS xQ /- sin xd 3.

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Q: 7. y = tan³ (2³) (A) 3x² sec(2³) tan(x³) (B)-3x2 sec(³) tan(x³) 8. y = cos(5x) (A) sin(5x) (B)-5…

A: Topic = Derivative As per guidelines, At a time only three sub-parts of a question can be answered.

Q: Find Y'and y" Y = sin (x²) Y = 2x² cos (x²) 2 y" = ? 2

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Q: find the volume of the solid

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

Q: -1 Differentiate y = sin (sec(4x?)). %3D 82 tan(4a?) sec(422) A. y' 1-sec2 4r2 8æ tan(42²) sec(4x²)…

A: We will find the derivative of the given function in the following step.

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

A: Use trigonometric substitution method for solving the integral.

Q: Evaluate sin (3x) cos (6x) dx Select one: cos(9r) A cos(3r) tC 18

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Q: pin z +y 12 + cos 2 2r F(1,y, 2) =- TY + 2,- + Cos 2

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Q: y = (sin x +cos x) sec x = sec² x

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Q: If 16(sinx)2 + 16(cosx)² 10 then x=.. %3D Зп/4 T/2 п/4 T/3

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Q: Find , where : = sin (x²) cos (y) COS 6.x sin (a) cos (y) 2.x sin (a) O2.x cos (2) 2r sin (2*) cos…

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Q: / – 9x* sin²(7y") = 9x* cos²(7y/") What is y(4) if y(0) = 8? %3D %3D

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Q: y=cos(4x) /cos22x-4sin2x cos2x differentiate?

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Q: 1) x² sin(y') + xe2 – cos(z?) = 3y– 6z + 8 cos(z?) = 3y – 6z + 8 %3D -

A: Given; x2siny3+xe3z-cosz2=3y-6z+8 Now differentiate partially with respect to x we get,…

Q: Find , where : = sin (a²) cos (y*) O 2.r sin (a²) cos (y²) O 2r sin (x²) 6.x sin (a²) cos (y²) 2x…

A: We have to find partial derivative of z  with respect to x.Given a function of two variables, ƒ ( x,…

Q: 32. a. b. f cos(4sinx - 1) cos(2sinx + 8) cosx dx is sin(6sinx + 7) − sin(−2sinx + 9) + C 1 1 12. 1…

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Q: 3. = Cos xsin +xax+a 5/2 3/2 1. Ans: Y= 4sin'x* sinx+ To CAx+4)^- Cax+a) 3.

A: To solve: dydx=cos3x sin2x+x2x+1 Solution Given differential equation can be written as: dy=cos3x…

Q: What is if z = x²y+sin(ry²)? %3D dz = 2xy + y? sin(xy') az = x² + 2ay cos(xy) 8z = 2xy + y cos(xy?).…

A: The given function is z=x2y+sinxy2

Q: y = cev2z + Cze + C3 cos(v2x) + C4 sin(/2x) + Czev3z + Cge + c7 cos(/3x) + Cg sin(/3x)?

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Q: 4  find The indefinite integral

A: To evaluate the given integral

Q: b) Is S cos4xv2 – sin4x dx = V(2 – sin4x)³ + C true or false? show me %3D

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Q: y" – 2y' – 8y = 3 cos 2x + 5 sin 2x

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Q: 1. [* sin' y cos' ydy 3

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Q: 5. y + 4y = sin x + 3 cos x Ans: y = C₁ + C₂ cos 2x + C3 sin 2x + sinx-cosx

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Q: What is r 1- O Option 1 2 2 sin 0-3 cos 0 3 y = ² x + 1 2 x² + y² = 2y²-3x Option 3 in Cartesian…

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Q: 1/2 sin 12 y cos' y dy y

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Q: 2 cos(플x-지) =D v2 TO

A: Given trigonometric equation is:  2 cosπ2x-π=2 We have to solve for x.

Q: i) L-- (In) L- | s-3 6s+3 ii) L-1 iii) L(tet cos wt) s+1 sª+5s2+4,

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Q: The period of y = 3 cos 5x is 2 2 /5 2 /3

A: Given that: y=3cos5x

Q: 2y 1 + cos 3x - 4.x + 3y sin 3.r = 0 %3D dr

A: 2y-1x+cos3xdydx+yx2-4x3+3ysin3x=0 Rewrite the above ODE in the form of Mdx+Ndy=0.…

Q: sin COS dx V 32 COS 35 5cos² + C O 32 COS 32 + 4 COS 4 口 32 cosS Ssin+2-c cos () + c 35 4 4 32 CoS 7…

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Q: 2- Calculate y": y = 5x2 Sin (3z) - 2x Cos (5x)

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Q: Given: cos 3y + sin 2x 2 cos 2x 2 O -3 sin 3y-3 -2 cos 22-2 O -3 sin 3y 3 O -2 cos 2x-2 3 sin 3y 3 2…

A: Given: cos3y+sin2x=2x+3y To find dydx in the given equation.

Q: y = cos (tan (3x)) A. -9cos? (tan (3x))sin (tan (3x)) sec (x) B. -9cos? (tan (3x))sin (tan (x))…

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Q: 1. dz (1² + 5)² 2. COs z dz 3. sin 3r cos 5z de

A: Given: I1=∫x3x2+52dx, I2=∫excosxdx, I3=∫sin3xcos5xdx

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

A: Topic = Derivative

Q: 4 2 cos y + sen²y cos² y - senty 3 cos² y 1

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Q: 1. Solve the DE: tan xsin y y'+(3 tan x-2 cos y) secx= 0

A: Given tanxsinyy'+3tanx-2cosysec2x =0 tanxsinydydx+3tanx-2cosysec2x =0 3tanx-2cosysec2xdx+tanxsinydy…

Q: (11). - cos?(2y) sin? (x), y(등) =0 Workings y= tan '(z - 글sin 2v) +

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Q: Find LT of (i) e-*(2 cos 5t – 3 sin 5t) (ii) e²ª cos² t (iii) e“ sin 2t cos t ,4t

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Q: 04.) Show that y = (sin x +cos x) sec x = sec² x

A: Given inequality does not equal. See the attachment