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A: The given differential equation is x''+4x=sin2(2t) First, let us find the complementary solution for…

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Q: - dx +3x+3 メstx a. 14 マ tan ()"० 3. 6. 9 tam- C.12 tan-l C d. 9 tan tc e- more.

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Q: Evaluate the followin dx X dx%3D X- 3 (Type an exact answer.)

A: Integrate as general

Q: d (arccot(x)) -1 Be sure to provide a written justification for 5. Prove your work. dx 1+ x2

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Q: EVALUATE USING HALF-ANGLE SUBSTITUTION dx 5 + 4 sin a A. aretan (Stan (3=) + 4 arctan +C 3 В. 2 5…

A: This question is based on indefinite integral.

Q: 25 – x² In -dx , if we let u=/25- x2 , then udu= – xdx. T True F False

A: Follow next step

Q: Given #= (1+--). dy 2 dx What is the value of k such that y is parallel to the curve y = 3x +1 at x…

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Q: Please answer parts a-b Suppose X has pdf: f,(x) = { { 2x, 0<x<1 0, elsewhere %3D Let y = e* + 3e*…

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Q: 1. So letet Jo 1+ e* t -dx

A: The given integral,        ∫01ex1+exdx

Q: Find dy/dx in terms of x and y if ax^3−by^4=c^3. Assume that a, b and c are constants.Thank you!

A: we have to find dy/dx and given that a relation between x and y As  ax3-by4 =c3  and a,b,c are…

Q: af af If f(s, t) = sin s cos 21, find and as at

A: fs, t=sins cos2t Partially differentiating with respect to s, we get ∂f∂s=cos2t·coss

Q: Q6. Let w = f(r,0), r = √x' + y³, 0 = tan'(y/x), ), find aw ?х > and ди ду in terms of r and 0.

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Q: If x>0 and arctan(x + h) – arctan(x) h 4 limp »0 then what is arcsin(x)? Lütfen birini seçin: Ο Α 2π…

A: Given: limh→0tan-1x+h-tan-1xh=47, x&gt;0 we know that given limit is derivative of tan-1x and…

Q: 4. dx + 2x = 2 x²y²dy %3D

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Q: Q/ Let w=F(Xi)) and X= V cose, y=Y Sine Show that (w 2 %3D Y

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A: The trapezoidal rule uses trapezoids to approximate the area: Where, .

Q: if y= Cot" (-+) y=Cot Prove that dy 1-x

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Q: 3. Use No. 2 to s subject to the g dy 2y – dx — е* 3 e = Your answer

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Q: Compat dx n=4 Trapezoida 1599780 Sinipson's exact

A: To Determine: Find the value of given integral by using Trapezoidal rule &amp; Simpson's rule.…

Q: (a) /(- cscr cot z – sin z) dæ: (b) | (x5 – 4x + 7)°(5xæª – 4) dx =

A: Solve it.

Q: Evaluate ∭x2 dV, where E lies between the spheres ρ = 1 and ρ = 3 and above the cone Φ = π/4?

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Q: Please answer parts a-b Suppose X has pdf: f,(x) = { 2x, 0<x<1 0, elsewhere %3D Let y = e* + 3e* a)…

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Q: b) Si Va dx. (Recall that x = Vra = (V)" so could you rewrite this as a x°?)

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Q: dy If tan y = X, then dis %3D

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Q: 10. Prove the following formulas : d cot u = – csc u. dx d CSC и 3 — csc и.cot и. dx 2 du а ) * dx…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: dy Find dx for 3" + 3" = 3(+9at the point (1, 1). 3(a+yat the point (1, 1).

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Q: 7 Let y Find values for A and B so that dy dx A where A B = || ||

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Q: у?dx + (ху — 1)dy %3D 0

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Q: S x dx/(x² - 3) = In]x? - 3| + c * %3D O False O true If y= csch3x then dy/dx = - 3 csch3x %3D…

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Q: (5 + sin r)e 2. If y = what is dy/dr? 12 - 7

A: Use basic identities of derivatives.

Q: Normal equatim? for the flang Find the Tangat, fonctinar ) fle> - 3X + xtomx dx- 写 2) 2y+TSing =2女…

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Q: d = e*, we must have that fe'dx = e*. Since dle)=e", %3D

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Q: determine an expression for dyl dx a)y= 2x*+ e*+ 2x² tan(x)+TT

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Q: f cos √2x dx

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Q: 1. Use Trigonometric substitution to evaluate f dx. Hint: Ju? – a² let u a sece.

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Q: Determine whether fhe e Xaut . i7 it is exact, solve it. given differental eguation tosk -2kg)…

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Q: Given that ƒ(1) = 5, ƒ′(1) = 4, g(1)= 2, and g′(1) = 3, find

A: Given- ƒ(1) = 5, ƒ′(1) = 4, g(1)= 2, and g′(1) = 3. To find- ddxfx·gxx=1 and ddxfxgxx=1  Identity…

Q: | x° dx from a=-1 to b-1 is an odd fur O TrS False

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Q: du -(cosh u) = dx "(sinh u). dx dx A True B) False

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Q: Q# Which of the following is equivalent to: xarctan(5x)dx = -dx 2(1+25x²) A) -arctan(5x) – | 5x B)…

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Q: Given f(x, y) = 7æ° cos (y*), find .9 COS fzy(x, y) = fyy (x, y) = %3D

A: Given  f(x, y) = 7x9 cos(y8) To find fxy, fyy

Q: Ⓒ'Evaluate Sot So Sox sing ²sin y dy dz dx tim of the

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Q: Find dy/dx in terms of x and y if ax^2-by^5=c^2. Assume that a,b, and c are all constants.

A: Given equation is-  ax^2- by^5= c^2

Q: az dz A. If Z = ey sin + ex cos then show that x + y ax = 0 dy B. If f = x?cosy + y²sinx then show…

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Q: 9) xdy- ydx = (x² + y ² ) ex dx a) artan. * =* b) arctan X = ţ c) auctan $ d) none of the above etc…

A: This is a problem related to differential equation. Based on the general formula and concept we will…

Q: x sect and y= tant, evaluate at t = - of the follow 4 dy (b) d y dx?

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Q: Find p, q if f," f(x) dx + Si2" f(x) dx = [,' f(x) dx. %3D (Give your answers as whole or exact…

A: Given,