1. Find the first-order derives: III. y = (2x* – 5)(3x5 + 12) IV. V4x? + 7+ 5-x° + 15x – 30 5x+ 4x3

Q: If -y = xy - 3x then find d at the point (-2,6) in simplest form. 1

A: As we know that the differentiation of:- dxndx=nxn-1 (fg)'=f'g+fg' fg'=gf'-fg'g2

Q: 2. -1z"cosdz zl=1

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Q: Find the arclength of y = 4x³/2 on 1 < x < 3

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Q: 2 Consider the hypocycloid with equation y 3 +x3 =73 2 2

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Q: Q.1A) Evaluate 2 (4-x*) 4 cosy dydx 4-y

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Q: Suppose that / (3x+-x²) dx=Ax³+ Bx³ +C, for constants A, B, C. What is the value of C if the curve…

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Q: Y Is the midpolnt of XZ.If XZ 8x-4 and YZ = 3x +1, find x.

A: Given Y is the mid-point of line segment XZ XZ = 8x-4 YZ = 3x+1   to solve the given question use…

Q: By Lagrange's formula, prove that y =y3-0-3(ys-y- 3) + 0-2 (y_ 3 -y_5).

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Q: state where in the ty-plane the hypotheses of Theorem are satisfied 7. y′=(t2+y2)3/2

A: Given y'=t2+y232

Q: Q2. Find of y = 4x/x + v at x=1? dr

A: We have to find the dydx of y=4xx+x at x=1.

Q: 6. Find the domain of y = Vx+ 4x + 5x + 2 + Jxl-|x+1]

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Q: z² - xy = 2 at the point (2, 1)= %3D

A: We have to find the slope of the line tangent  to the given curve.

Q: Find the point thot maximites the f (xxy)= x*+ y 2. -6x+ 9 funcfion depending on the gCxy) zy -x²…

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Q: 4' for T- T2• T, and T- T1• T2. x - 5y, 4x + 2y) y, 0)

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Q: Determine the interval in which solutions are sure to exist. y(4) + 5y" + 3y = t Valid on the…

A: Given differential equation is y4+5y''+3y=t. We have to determine the interval in which solution are…

Q: 9. Find the characteristics of the equation pq = xy %3D

A: Given that pq=xy The given equation can be written as px=yq=a(say) Therefore,  px=a ⇒p=axdzdx=axyq=a…

Q: z = 6x + y2 tan 4

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Q: 6. x = t and y = 3t – 2 for 0Sts4 %3D -

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Q: 4. Find dyax and d2 x =V4- t , go t²-2t ye t'-2 get'.

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Q: Use the diffecential equation dy= and the initial condition. y=(9)%3T. Fad funchion of 81.

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Q: Find the arclength of y = 3x3/2 on 2 < x < 4

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Q: 1. Solve for the othogonal trasctories y =x²(1-cx)

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Q: Use variation of parameters to pind Yr F -2xy' +ay: -12 x) given that = x and Yx art solutions of…

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Q: Find the general solution of ylty = 2xcosx -cosX %3D

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Q: The arclength of y 4x/2 for 2 < r < 4 is:

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Q: Suppose that 4x² + 2y² = t² and y=tsin 0. Find ду (27) ət 0 and at ?x

A: The given equation is y=t sin θ. Consider sin θ is a constant term.

Q: 1. (D 2 + 3D + 2)y = 4t 2 By: (a) reduction of order, and (b) variation of parameters.

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Q: Graph the curve. O r = 6 + sin(40) -6 -4 -4 y 2 2 4 4 X BB÷ 2 4 -6 -4 -2 -4 -2 2 -6 2 4 6 X

A: The given function is r=6+sin4θ To find: We have to find the graph of the given function. We have…

Q: 3 a AB: 4x + 5y = 13; midpoint (2, 1)

A: The equation of the line is 4x+5y=13. The midpoint of the line is 2, 1.

Q: G7. Find yet), the solutlan of the interval value problem 4'=-2t +2te, ylol= 0 -2t2 ulol= Y09 where…

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Q: Use undetermined coefficients to find the particular solution to y''−9y'+20y=−1768sin(t)

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Q: Is the equation t²y' (1) t + 4 - separable? y?

A: t2y't=t+4y2

Q: - z²) – 2x + 30y = 0 da? What is the larger root from the indicial equation

A: Given differential equation, 1-x2d2ydx2-2xdydx+30y=0 Find the largest root from the indicial…

Q: Find the arclength of y 4x3/2 on 1 < x < 2

A: Here in this question given that y=4x3/2 and find the arc length. Between x=1 to x=2.

Q: Find the arclength of y 3x3/2 on 1 < x < 3

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Q: is the minimnurm step of the horno gone ous n What X+ xt 2-X ifferential equatian with its solution…

A: The objective is to find y=x2e-x+x3+x2what is the minimum step of the homogenous differential…

Q: ) Let Z = 3x2 – y². Find all points at which |VZ| = 6

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Use the substitution y = xm to find the general solution to: x2yn - 2xy' - 4y = 0. Show all of…

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Q: Use undetermined coefficients to find the particular solution to y'' + y' – 3y = 4t + 5 Yp(t) = %3D

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Q: Sketch Z= 2x^2+3y^2

A: To sketch: Z=2x2+3y2.

Q: Q1: - find dylar for y = 5cscx3

A: Dear student as per our rule in one session we can only solve one question. Please post the other…

Q: dx Calculate for n = 6, using trapezoidal rule. %3D -11+ x²

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Q: A 3 X Y- X Y = 4xソーメニ2findr 3D2 and X"at X =1

A: Using definition of differentiation

Q: 4. Determine the unknowns using [X] = [A]¯*[B] and [A] by the adjoint method. %3D 10x + 2y – z = 27…

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Q: Find the first approximation to the root of the equation x - 2x- 5 = 0using Regular-Falsi method…

A: Intermediate value property: Let f(x) be continuous function in a,band if f(a)&gt;0, f(b)&lt;0 then…

Q: c. Reflection over the x-axis and a y- intercept of 5

A: Given the attribute :

Q: If x) is shown below 3 Then y(t) x(3t – 3) – 1 has the shape

A: Kindly go through the solution and let me know in case of any doubt or further clarification in the…

Q: Find de máximum and minimun of the equation f(x)= 2x^4+x^3, [-4,-1]

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Q: find the first order linear y(t)=4et-1-t-1

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