d. y=cos° (x² +3) s" (x² +

Q: 3. S sin®2y · /cos2y d|

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Q: dy If x=5+cos20 and y=3- sin20 , what is ? dx

A: The solution for the above question is as shown below.

Q: Approximate (a) cos 0.8 and (b) cos 1/2 using the linear approximation technique

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Q: b) S sin 2 x cos x dx

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Q: d²y If y=cos 4xr, then at x = 0 dx?

A: Given,     y=cos4x

Q: 211 2E1 sin nx dx | cos nx dx 0, where n integer. 22

A: We have to show that

Q: Eliminate the Arbitrary Constant •y= C, e¨cos3X + C, e**sin3x •y. Ac" + Bxe* y: x*+C,c" + C, e**

A: soln 1 y=Ae2x+Bxe2x    diff with respect to x∴y'=Ae2x(2)+Be2x+Bxe2x(2)…

Q: a) y = sin x² cos 2x 4.

A: Given: y=sinx2cos2x, y=cos4sec23x We know that ddxuv=vdudx+udvdx…

Q: H 2= x? tan y/ at (lo1) %3D Ex by

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Q: (e² sin*(2r)' 21² +1 , y = In

A: Use the lograthim rule of derivative and than with the help of chain rule calculate the derivative…

Q: // Show that y" + y = 0, given that y = 2 sin x + 3 cosx

A: First find the first and second derivative of the given function then simply put and simplyfy

Q: Show that y" + y = 0, given that y = 2 sin x + 3 cosx

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Q: The position of an object attached to a spring is given by (t) 3 cos(4t) – ¿sin(4t). where t is time…

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Q: If y = cos(sin(2.x)), find . dx

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Q: In y = C, sin 8x + C cosax + 9x²- 2

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Q: , Sercoszx *cos2x dx 3.

A: Since multiple questions are asked answering the first question, repost other question for solutions

Q: I= ( cos(In(x)) dx 13- I =

A: GIven that: I=∫cos(ln(x))xdx

Q: Show that COS x dx a² – x² sin a 2а where a is some positive number.

A:

Q: find dy. = cos (x2)

A: Given- y=cosx2 To find- The value of dydx. Formula used- ddxcosx=-sinx.

Q: Demonstrate and derive the following Bernoulli's Equation. - 2y tan x = y² tan²x dx

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Q: Use this equation to find dy/dx. 4y cos(x) = x² + y2

A: We will differentiate  equation with respect to X.

Q: If S sin 2y cos 2y dy = =, then x is equal to: %3D

A: Hint:    sin2θ=2sinθcosθ

Q: Find dy. y=cos(7 *square root of X)

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Q: dy 7. Find ,y = cos³xsinx? dx

A: Given: y=cos3xsinx2 Formula used: Product rule of derivative: ddxf×g=dfdx×g+dgdx×f Power rule of…

Q: dz Find a? sin(2y – 5z) =1+y cos(6zx)

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Q: cos 2y dy sin y

A:

Q: A particle moves in the xy-plane so that its position at any time t is given by x= cos(5t) and y =…

A: According to the questionx=cos5ty=t3

Q: find dy for ee Sin (メ+34) dx

A:

Q: Show that r = cos(2pi) is symmetric about the y-axis.

A: The solution of the problem is given in the next step.

Q: Find the solution of d2y/dx2 +4y=sin3xx+cos2x

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Q: Solve the DE when all conditions set to zero. (D² + 4)y = sin²2x

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Q: Find (d^(2)y)/dx^2 if y=sin(x)cos(x)

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Q: d (cos – sin) dx 4

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Q: 211 2E1 sin nx dx = cos nx dx 0, where n integer.

A: To show that ∫02πsin nx dx= ∫02πcos nx dx=0 Where n is integer.

Q: (D² – 3D + 2) y = 14 sin 2x – 18 cos 2x

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Q: S cos(e) In (sin(0))d0

A: We take the help of integration by parts in solving this problem

Q: a) cos(xy)=2y, find y' DI y = cot-1 1+x 1-x

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Q: Find y" at (2,4) for cos(x²y + 5) = 16. %3D

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Q: t/2 SL cosx/1+ cos²xdxdy is equal to 0, siny

A: Consider the iterated integral, ∫ab∫f1xf2xfx,ydydx In this iterated integral, the integration is…

Q: 3. Find d, where ; a) cos(xy)- (x+y) (x+ =2 + e

A: As per bartleby guidelines, for more than one question only 1st one is to be answered. Please upload…

Q: Find a/dx2 at the given point without eliminating the parameter. *=0+ cos0 and y =1+sin ; 0 =n/6

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Q: y = In(cos“ x ) %3D

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Q: (b) Determine cos(x²) 2x dx by using substitution method.

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Q: Find an equation such that y xe" cos(2x) is its solution.

A: To find an equation we derivative both side with respect to x.

Q: dy Solve cos x(e2y - y) - dx = e' sin 2x,

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Q: y 3x+ 6 cosx, 0 £xs 2n

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Q: da (cos ( 3x) sin( 2æ)) dæ

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Q: The integral . (cos(3x))'sin(3x)dr under the change of variable u = cos3r becomes v u'du. 9/29

A: