IT 5. h(x)=cos x+ 2 n(x) -(х-3)* +4 6. 7. W (x)=e**2 –3 x+2 8. f(y)=(y-1) +2

Q: 3 S² x³ cos x ²dx 6.

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Q: 1 - cos(3x) lim 3x х> 0 1 + Зх — е e

A: We , have                Given      lim 1-cos3x1+3x-e3x     x70We have to evaluate the…

Q: Find general Solution of DE =0 on Co, mo). AISO how that xJú (x)-VJ,(x) + x Cn)

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Q: 2 lim In (cos x)e

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Q: S 4- e-2) cos(e- + In z) dz

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Q: 1. f(x) = sin 2x + cos 3x + x² = 0 with xo = -0.5 , Ax 0.1, TOL = 0.001, in [-0.5,1] %3D

A: Given equation is fx=0 where f(x) is defined by fx=sin2x+cos3x+x2  Given initial solution is x0=-0.5…

Q: In y - e* + 2cos z = -3 In y +3cos z = 4- 2e* 2) e2x 1 +3 = +ln(z ex cos z +

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Q: Obtain a differential equation associated with the primitive Ax2 + By2 = 1

A: See answer below.

Q: 4. The value of fx sin(x²+3) dx Acos (x²+) + C C. cos (x²+)+C B. -cos (x²+)+C D. -cos (x²+) + C

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Q: 2. f(x) = x²cos 2 x 3. f(x) = tan x – sec x sin x 4. f(x) = 5. f(x) = 2cos (2 + x³) 6. f(x) = x²ln x…

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Q: Q1: - Use N.R.S. Method to solve the equation f(x) = e-* - cos x start %3D with x0 = 1 and use four…

A: It is given that

Q: Suppose that Mdx + Ndy 0 is an exact equation, and M and N are both homogenous functions of degree n…

A:

Q: 6. Suppose you wish to differentiate g(x) = sin²(x)+cos²(x). What is the fastest way to do this, and…

A: Given,

Q: Sf(x) dx = 1 0.694 (sin(x) dx = 1 0.694 COS TX T C = 2 C 0.694 How? ==→ 1-C05 (0.69471) = 1694 -

A: To determine the value of C .

Q: In( cosh(11x) - sinh(11x) )= Select one: 01 O11 sinh(11 x )+ 11 cosh(11 x) O None O zero O-11x O11x

A: Given: lncosh(11x-sinh(11x)) We know that   cosh(x)=ex+e-x2        sinh(x)=ex-e-x2   Then…

Q: -1-3x+ e3X ) im x>0 hint: L'Hopitals Rule - cos(x)

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Q: 8. lim,0 1-cos x 2x2 1 (a) 1 (b) – (c) 0 (d) ; (e) 1. -

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Q: E(- 1y**cos(nx) n=1

A: see 2nd step

Q: 1+2 e-kt cos kx = k=1 sinh t - cosht cos x

A: To prove / disprove: 1+2∑k=1∞e-ktcoskx=sinhtcosht-cosx

Q: 2. 1- x2dx cos(x + 1) dx 3.

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Q: 4.4. Show that the function f(x) = Sx² cos 1, if x = 0, ૨૦. if x = 0 is a BV-function over the…

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Q: X 1) f(x) = x6 + 4x + 2 I NIX - 3) f(x) = ln(x5 - cos²x) 5) f(x)=xsin x + πT x5 -√x - In 3 3 2)…

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Q: 7). Suppose a is a positive constant less than T. Prove that the equation 2x+cos x = a has a real…

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Q: INTERGRATE THE FOLLOWING: -0.33 (1). S [8.5244 x 10 (1 – cos(4.759x)] dx ,0.33 (2). [8.5244 x…

A: It is an Integration problem. I used substitution method to solve the second question. I  evaluated…

Q: Obtain a differential equation associated with the primitive Ax^2+By^3=9

A: Differential equation is obtained by eliminating the constants A and B from the primitive equation.…

Q: 3. Find the critical numbers of the function f(x) = sin2 3x + cos 3x , 0 <x < 2/3:

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Q: -x² 9 d. f (x) = xe [0, 5]. e. f(x) = |x² − 4], [0,3]. sin x f. f(x) = = [-ㅠ -π, π]. x² + 1

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: We have determined that g'(x) = 2 and h'(x) = cos(x), where g(x) = 2 In(x) and h(x) = sin(x).…

A: Our Objective is to find the derivative.

Q: Find the solution for cos(x)" - (1 + x²) – 2xy = with the conditions dx2 1+x2 y(1) = -1, y(2) = 2…

A: Given equation is  cos(x)d2ydx2-(1+x2)dydx-2xy=11+x2 with y(1)=-1 and y(2) = 2 h = 0.25 To solve  -…

Q: Find the solution to the initial value problem for f(x) = 0 and g(x) = 2 cos 5x. a2. - 00 0, u(x,0)…

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Q: Given In = S cos" x dx = - cos"-1 x sin x + In-2 ; %3D n/2 determine a reduction formula for cos" x…

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Q: 1. Suggest ways to avoid loss of significance in these calculations. (a) √√x4+4-2 (b) ln(x+√x² +1)…

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Q: 2 2メ Q1 find dy for y = Cos ( In x + e

A: we have to derivative with respect to x

Q: 4) f(x)= cos x COS X %3D (5) f(x)=xsinx -1+ Cos nx

A: Since you post more than one question. As per our guideline we can solve only first question for…

Q: Find the general solution using reduction of order. 1. y''+y'=cos(4x)

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Q: too ·00 dx COSX x² +hx+5 =le Residue solution cos (2)

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Q: 3 f(x) = x° – cos(x) %3D х — - Solve this question by the Fixed-point method on the topic of…

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Q: Aitken acceleration method

A: Given: A function is given by f(x)=1-4x cosx +2x2+cos2x To find: The solution of fx=0 starting with…

Q: Thus, for u = g(x) = sin(5x), %3! f'(g(x)) = F'(sin(5x)) = 8 %3D %3D 8 Next we calculate g'(x). g(x)…

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Q: 2. Solve the initial value problem f"(x)= 2cosec3xcot3x +5 cos(-x)+3, given Зл = 4 4

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Q: 55. f(x) = x² + cos ¹x on [-1, 1]

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Q: 0<x<T (-1)"-1 f(x) = { 27-x COS nX n<x< 27

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Q: 1261 (2x+1 dz 4-3x -x² 1 (((x+) dx (3) 28 (2x-3 dx √(x²-1) (2x+3) 31 32 33 dx √(x²+1) (2x+1) alx…

A: Note: As per Bartleby guidelines only the first question has been solved. Given: The function is…

Q: - 7x +2 g (x) = (x + 1) (x – 5) h(x) = -2 cos x+5 y = 4(x + 1)³ –7 x2 y = 4*+2 f (x) = -3x° + 6x¬² –…

A: To organize the following equations a polynomial or non polynomial.y=15x4-7x+2gx=x+1x-5y=5x2hx=-2…

Q: 3. Given that 2 = 6²¹ sin (u + ), e2v Use chain rule to find az/0x when x = 0, y = 0. u=e¹ - sin (y…

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Q: 4. f(x) = 2 cos(x – 2n)

A: Given:  f(x)=2cos(x-2π)

Q: Find the solution of the equation zxx + zyy =e-xcos(y) which tends to zero as x-> ∞ and has the…

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Q: .2 Suppose that w = x² + y² – z2 And x = psin(4)cos(0), y = psin(4)sin(0), z = pcos(4) Use…

A: The Solution is given in next steps

Q: 5.f(x) = x (x - 1)(*- 2)(* + 1) As x + +o, f(x) = As x - -n, /(x) As x > I co, f(x) – As x > w./(x)…

A: Solution is given below:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.