(2823 у — 3D 252*у — 6 sin 3а) dx (20x°y3 – 21a*y?) dy 4.4 - -

Q: . If y = tan( sin t (. cos t-1 1 dy %3D show that dt 2

A: The given details are as follows. y=tan-1sin tcos t -1 Observe the chain rule of differentiation as…

Q: dy 13 %3D - dn Solve this by using Bernoullis eajuation?

A: Given differential equation is: dydx=y(xy13-1)dydx+y=xy141y14dydx+1y13=x                         (1)…

Q: The linear approximation at x = 0 to sin(2x) is A + Bx where A is: Preview and where B is: Preview

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Q: Suppose that y = 4 cos² t , x = v3 sin(2t) and 0 < t<a. Then dt2

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Q: O. p. S sin 2x cos 3x dx 3dx /1 + 9x²

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

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Q: 2 sin? 11. y = 3x 2x2 12. y = cos°V2x – 1 3. 13. у %3D Vtan(х?)

A: As we know that; The chain rule: fgx'=f'gx·g'x The Quotient rule: fg'=f'·g-g'·fg2 The Power rule:…

Q: 4) a²y=+52y =14 yat (2,1) Find equátion of tangent?

A: Equation of tangent  y-y1=m(x-x1) (x1,y1)are the points at which equation of tangent is to be…

Q: If Sin-'x= Iny, show %3D ( l-xx) day - dx d X 2 x dy =y

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Q: The approximation of I = = co cos (x²+5) dx using simple Simpson's rule is:

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Q: tan (VT)+2 dx J Va (sec(VT) – cos(/7))

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Q: Let 5 sin æ + 6 cos y = 6. dy dx d?y dx?

A: 5 sinx +6 cosy = 6  Differentiating w.r.t x,  5 cosx +6 (-siny) dy/dx = 0  dy/dx = 5cosx/(6siny)

Q: 1 1 S [ sin(1+ y²)dydx= 1- cosl a. 2 cos 5

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Q: sin(2t + ) dt = 00 64e 4. O O OG

A: Here in this problem we have to find ∫0∞sin(2t+π2)e2t-3dt

Q: it Z = exY , where : x= Incutv) and y = tan () %3D find a) du శ్రీశర శశ్ర

A: Given,  z=exy ; where x=lnu+v and y=tanuv To find: partial derivatives

Q: If y = (4x) sin ( 3z) then %3D dy dx (Be sure to express your answer in terms of x)

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Q: If y = (3x)sin (2æ) then %3D dy dx (Be sure to express your answer in terms of x)

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Q: sin(2t)dt 0,

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

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Q: -1 Suppose y = sin ¹x. Then y arcsin 1 Oy= sin a Or = siny Or=

A: Given that:- y= sin--1x. Then  Topic:- inverse trignometry

Q: The linear approximation at x = 0 to sin(3x) is A + Bx where A is: Preview and where B is: Preview

A: Given function:

Q: dt cos (2 sin 21) /1– 4r

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Q: Integrate with respect to x: sin(3r) b 2 cos(4x) cos²(2x) a

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Q: To evaluate 3cosx -1 1- sin?x dx, the integrand can be transformed to A J(3 cos x - sec²x) dx ® S(3…

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Q: 3. Integrate the following dx (i) V9 – x² (ii) ſe-3*cos4x dx (iii) ſ sin³2x dx -

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Q: in integrating the function fx cos() dx using intogration by parts, whut would you choose for your…

A: Solution

Q: 1 Cos(2x)dx 0. (i) Using composite Trapezoidal rule with n = 2, 4

A: As per the policy of bartleby the provisions is to solve only one question at a time So I am solving…

Q: dy dx a) { In |0* + 1|} „b) arctan (ve2 -1) , c) sec-(0²) – 1

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Q: Find the value of dy/dx at (1,0) of 2re" – In() = 4y² + 2a sin

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Q: arctan(*) 1+e2kx dx =? A) arctan(e*)In|cos(arctan(e*)| + S in |cos(arctan(e**)dz]+ c kekx 1+e2kx B)…

A: ∫arctan(ekx)1+e2kxdxFormula to be used :1.Intergration  by parts2.Substitution3.ddxarctan(ekx) =…

Q: 11. Put the following equation in separated form, do not integrate. do d. + sin 0 = 0 %3D dt

A: Topic - differential Equation

Q: arcsin 4y dy 1 – 16y2

A: Given: ∫arcsin4y1-16y2dy

Q: Find ds/dt if 3t + 3s sin(3t) + 3cos(t) %3D

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Q: 17. Determine the value of fx dy - y dx, where x(t) = (cos 31, sin 3r), 0 ≤ ≤n.

A: The given integral is: ∫X x dy - y dx, where Xt=cos 3t, sin 3t, 0≤t≤π The components of the…

Q: ACTÍVITY 2: Differentiate the 1) y = -2 sin 2) s (t) = - WE

A: Apply the differentiation rules for the trigonometric functions to get the derivatives of the given…

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

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Q: 10. J(3x3 — 5х + sin3x) dx -

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Q: Find dy/dx for 4 cos4 xsiny = 15

A: d(uv)dx=udvdx+dudxv

Q: 7T, 0 cos( {*) cos(2y)dx 2gin( gx) sin (2) dy 77

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Q: find dy dx ² +F y = 3 casch + Cosa 3 and x = Sin²³ o

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Q: 4 sin' 2x cos 4x dx 4.

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Q: 2n Sin (3y) dx + 3x Cos(ay) dly =o

A: Given differential equation is 2xsin(3y)dx+3x2cos(3y)dy=0

Q: The linear approximation at x = 0 to sin(6x) is A + Bx where A is: Preview and where B is: Preview

A: First of all, consider the formula to find the linear approximation at any point a for function any…

Q: B\ Suppose that = 4 cos² t , x = d²y =- V3 sin(2t) and 0 <t <n. Show that sec3 (2t). dy 2 tan(2t)…

A: Dear student, there is a mistake in the question. The second derivative should be…

Q: 12) / Зy sin(5y?) dy

A: Solution:

Q: dy 1. sin 2ycos2y

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Q: sin(20nnt) ass A: AS(t)ln:0dd En=1 %3D %3D1

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Q: The integral (cos(3x)) sin(3x)dx under the change of variable u = cos3xbecomes v uz du. -9/29 Select…

A: Given,

Q: d. a) dt [8 sin 1 2t] = d. b) |7 cos s 1 5 dx d. 3u] = -1 c) 10 sec du

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