Find one root of the equation below f(x) = cosx – x %3D using HIM and SECANT method of x = 0 and x = 2 with dk < 0.006. %3D 2.

Q: Find an interval of definition for the equation x^2 dx/dt = 3x^3 t^2

A: Domain of definition is where X(t) is defined

Q: Find the value df (a) that Make ECX) is Contincity at X- Ž

A: Given that :f(x)=cosx2x-π      ,             x≠012a2-3a+4      ,   x=0

Q: if f(x)=2x-cos(x), Use Newton's method to approximate x, starting from the initial value xo=0

A: Solution:-    fX=2x-cosX           x0=0    f'x=2+sinxwe know      x1=x0-fx0f'x0           =0-f0f'0…

Q: Find for the following function: dx 1- y = sin-1 V2x + 3 2- y = 3cot(cosx) 3- y = x*y at x = 1

A: We have to find the derivative of the following functions.

Q: find dy/dx for the function ex+y+2x-3y=e using implicit differentation.

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Q: Find dy/dx by implicit differentiation. VIY = r°y+66

A: givenxy=x5y+66diffrentiating by implicit method on both sideddx(xy)12=ddx(x5y+66)

Q: Estimate S, cos(4x)dx with Trapezoidal Rule. n = 10

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Q: Find the local linear approximation of cos x at xo = cos 61°. T/3 and use it to approximate

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Q: Determine the anti-derivative of Y = 2e3x +5 and use the fact that y(0) = 7 to %3D dx determine c,…

A: We first separate the variables and then integrate  c= integrating constant Formula used:

Q: sin(2t)dt 0,

A:

Q: Solve dy dy +y = 2sin(3x) dx? dx using the method of undetermined coefficient.

A: Given that,d2ydx2-dydx+y=2sin3x We need to find the solution of the given differential equation…

Q: find dy/dt. y = sin (cos (2t - 5))

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Q: Integrate the function. 8 dx V36 - 64x2 X+ C sin-1 + C -1 + C D 4 tan-1 3. B

A: Given:       ∫836-64x2dx  substitute u=4x3→dudx=43                   dx=34du         =∫636-36u2du…

Q: 8x 4х Q5. Use integration by part to evaluate fe* sin (e** )dx

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Q: (2х — Зу)dx + (2у — Зx)dy %3D 0

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Q: 34. ey sin x = x + xy

A: Given: eysinx=x+xy

Q: Calculate | e* cos(T2) da using integration by parts as many times as necessary.

A: Find the integration of excosπx using integration by parts

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

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Q: Find DE using variable separable cos/dx + 1/ydy=0

A: Given that: cosxdx+1ydy=0

Q: Solve using the integrating factors by inspection (y²-3-x) dy + ydx =0

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Q: Find the solution of the equation in the interval 0"sx <360 1. cos x+) 3 = - cos x +T3%3D

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Q: Estimate 1 7 cos(x2) dx 0 using the Trapezoidal Rule and the Midpoint Rule, each with n = 4. (Round…

A: I=∫017 cos (x2) dx             f(x)=7 cos (x2)b=1, a=0, n=4h=b-an=14=0.25aThe Trapezoidal…

Q: find function y =f(x) Satisty ing given equation. %3D and the prescribed initial candition dy CoS…

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Q: Use variation of parameters to find the particular solution to y"+y' – 20y = - 3400 sin(3t) Y(t) = |…

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Q: Solve the equation xcosy dy+(x+2)siny dx=0.

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Q: Given that xyt – 6 = 0, find dy by implicit differentiation. - %3D dx? dy dx?

A: A detailed solution is given below

Q: Find by implicit differentiation. dx 5 + 3x = sin(xy²) %3D dy Answer: dx II

A: 5+ 3x = sin (xy2)

Q: Find the solution of the DE using reduction Order (D2 + 4)y = sinx

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Q: In integrating the function f(3x + 5)(cos ) dx using integration by parts, what would be your du?

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Q: dy Q2) Find by using Chain Rule for y = sin34t dt

A: dy/dt for y= sin34t

Q: The approximation of I = f(x-3)** dx by composite Trapezoidal rule with n=4 is:

A:

Q: dy Integrate dx = 4e®xand find equation of curve that passes through the point (1,7).

A: Given that, dydx = 4e8x

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

A:

Q: The of the function y= e sin(3x)- In(5.x +2x+1) dx at (0,0) is: А. О В. -1 С. 1 D. 3

A: Dear,as per company guidelines we can answer only one question at a time, kindly post other question…

Q: (2x sinh2 + 3y cosh?) dx – 3x cosh dy = 0 |

A: Concept Used: For  y'=f(x, y)   ...(*)If f(hx, hy)=hn f(x, y)Then (*) is homogenous equation of…

Q: (c) Solve the IVP x(1- siny)dy = (cosx – cosy – y)dx.

A: Given,          x(1-siny)dy=(cosx-cosy-y)dxand            yπ2=0

Q: Solve dy dy + y = 2sin(3x) - dx? dx using the method of undetermined coefficient.

A: We solve the given differential equation by method of undetermined coefficients.

Q: Use the Euler method with dx = 0.5 to estimate y(5) if y′ = y2/sqrt(x) and y(1) =-1. What is the…

A: Consider the formula used in Euler’s method.Also summarize the given data in the question.

Q: Use the composite trapezoidal rule with the step length h = 0.1 to evaluate sin x = 5.² in six…

A: Given integral is ∫0πsinxxdx. We have to evaluate the given integral by using composite trapezoidal…

Q: Find dy dx for sin(xy) + y³ = x² + 1 and use it to find the equation of the tangent line at the…

A: use differentiation for finding the equation of tangent line.

Q: ydx = x(1+ xy4)dy

A: Given ydx=x(1+xy4)dy ⇒dxdy=xy+x2y4y⇒dxdy+x-1y=x2y3

Q: Use the trapezoidal rule withn= 4 to approximate cos(x) dx Keep at least 2 decimal places accuracy…

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Q: Find dy/dx by implicit differentiation. y cos(x) = 3x2 + 5y2 %D y' = II

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Q: Use Euler's method (with all details) to find approximate value of = 2y - 2x² -3, given that y = 2…

A: Given: y'=2y-2x2-3 , y(0)=2 , h=0.3. We find y(3) by using Euler's method. The formula for Euler's…

Q: 17. 2y° +4x2 - y =x° ² - y=x` +sin(3x)=12–j 4

A: We need to find implicit differentiation of : 17. 2y3+4x2-y=x6 18. 7y2+sin(3x)=12-y4

Q: Use Variation of Parameters to solve the DE y" – 4y %3D

A: Given differential equation y''−4y=e2xx Write the auxiliary equation m2−4=0 ⇒m2=4⇒m=±2 Hence,…

Q: Find dy/dx at the given point without first solving for y. x2 — бу — 37 %3D0 at (1, -6) | dy dx

A: This question is based on derivative.

Q: Find the slope of the graph of cos(x + y) = 2x at the point ( 0, T1/2 ). Hint: Differentiate…

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