4 – 3y² – y* y-2 6 – y – y² 23 – 7x² + 14x – 8 1. lim (1+ Vw)(2 – u² + 3w³) 5. lim t² – 1 2. lim t+-2 t² + 3t - 1 6. lim 2r2 – 3x – 4 (2z + 2²▼ 2² + 4 V² + 3 – 2 x² + 1 V2r – V6 – x 4+x² 3. lim 2+2 7. lim 2 – r - 2 4. lim z40 3 – 6x² – 7x + 1 8. lim

Q: Xn Xn=3-(-1)" Xn = cos (¹) √1+n² Xn= 2n-5 Xn = where (yn) is bounded 4 Xn = n(1 + (-1)") + n ¹((−1)"…

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Q: I need help with 17

A: To find the 3rd degree Taylor polynomial T3x centered at a =2 for the function fx=ex5.

Q: 1. Find the Wronskian for y1 = x, y2 = x² and y3 = x³. 2. Find the Wronskian for y1 = sin 3x , and…

A:

Q: The domain of the funsfon f(x) te 9) E2,21, or equivalenfly,t243 C) [4,00, 0r )(00,4),or…

A: This question can be solved by applying the concept of existence of function at various points on…

Q: 1. A function f(x, y) is homogeneous of degree 7 in x and y if and only if, 2. The function f(x, y)=…

A: Definition of homogeneous function:- A function fx,y is said to be homogeneous if i an be written as…

Q: 1. Use the Chain Rule to find dy in terms of r. dr а у — (и—2)3 and и- 2x +1 b. y = Jū and u= 5z2 –…

A:

Q: A. Yp(x) = Ax² + Bx + C, B. Y,(x) = Ae², c. y,(x)= Acos 2x + Bsin 2z D. yp(x) = (Ax +B) cos 2x + (Cx…

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Q: Use Euler's method with step size h = 0.2 to approximate the solution to the initial value problem…

A:

Q: 2 (i) The function f is defined by f(x) = x2-1 (a) express f(x) in partial fractions. Hence, (b)…

A: We have the function f(x)=2x2-1, We have to answer the following...

Q: 4. If f:1 → R is differentiable on I and g(y) = yn for ne N and ye R what is (gof)' by usin chain…

A:

Q: 5x*e", 0S1 y(x) =

A: Given

Q: 2. The graph of y = cosh a is (a) concave up on its entire domain because y" = coshr > 0 for all r €…

A:

Q: Find L(x). 2y -a = 3t y+z' = 3e z (0) = y (0) = 0 = (x) T0 (s+1)(s–2)(s²+1) OL(z) = 3s2 3(s-1) %3D…

A:

Q: 1. A function f(x, y) is homogeneous of degree 7 in x and y if and only if , 2. The function f(x,…

A: Topic:- calculus

Q: 7. Evaluatexyddx+e*dy where C goes along the x-axis from (0,0) to (2,0) and then along the parabola…

A:

Q: 1-6 Use an appropriate form of the chain rule to find dz/dt. 2. z = In(2x² + y); x = /i, y = 12/3…

A: Given: z=ln(2x2+y);  x=t , y=t2/3To find:dzdt=??

Q: 1 2 cos (5x) cos(3x) dx = cosh' (In x )sinh (In x) (A) (C) (A) de= sinh" (in x} (A) cosh (Inx)…

A: Let's solve partial fraction.

Q: 7) Suppose w=rt+rs' and r= tan-' (2x² +3y), s=x²y' +3y and t = x²y² .Use the chain rule (from…

A: Given w=r2t+rs3r=tan−1(2x2+3y)s=x2y3+3yt=x2y2

Q: 3. x + y- 2z = 5 -x + 2y + z = 2 2x + 3y z = 9 Her sul - ng 5. 2x + y - z = 9ation, -x + 6y + 2z =…

A: If AX= b is the system of linear equ and we have to solve it by using the elimination method then…

Q: (D2 – 1)y = 2 2t -4 0st<2 %3D t22 y(0)=0, y'(O)=1 Find L{y} L (y) 4 2e -2s 6e-2s s2 (s² –1) s(s2 -1)…

A:

Q: 1. y" - 2y' - 3y = 5e¹, y(0) = 1, y'(0) = 0 2. y" + 2y + 5y = 3 sin(2x) 3. y" - 4y + 4y = -7x+4x²,…

A: Since you have posted multiple questions. As per guidelines we"ll solve only  first question. If you…

Q: Using Gauss-Jordan Reduction x+ y + 2z= -1 1.1 x - 2y + z = -5 3x + y+ z = 3 [1 1 1: 01 1 1 0: 3 1]…

A: As you have provided multiple questions with subparts. We will solve the first question with…

Q: 1. f(x, y) = x2 + y² –1 2. f(x,y)= 3. f(x, y)= Vx+ y² +4 5. f(x, y)= In(xy) 7. f(x, y,z)= sin(xyz)…

A: Vf(x,y) =[d/dx(f(x,y) ,d/dy(f(x,y)]

Q: (2t - 4 0st<2 (D2 – 1)y =- 12 %3D t22 y(0)=0, y'(O)=1 Find L{y} L (y) = F1) 4 2e-2s 2e-2s %3D -…

A:

Q: Show that the solution of initial value problem: d^2x/dt^2 + w^2x = F0cosAt, x(0)=0, x'(0)=0 is…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Xn Xn=3-(-1)" xn = cos (¹₂) √1+n² Xn= 27-5 Xn=¹ where (yn) is bounded 4 lim inf(x) lim sup(x₂)

A: We know the fct that for every  bounded  sequence  limsup(xn) and  liminf(xn) exists finitely. since…

Q: y′=−28y+2sin(2x),0≤x≤3,y(0)=4.

A: Given: y'=-28y+2sin2x,     0≤x≤3,y0=4

Q: The equation y' = 2 (In y- In x+ 1) jis ? First order, Partial. First order, Homogenous. First…

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Q: If q x2 yz3 %3D =, the small increment in q with &r=8y=8z=±0.1 can be approximately calculated by…

A: We will use partial derivatives to calculate the required quantity.

Q: Solve this equations by using homotopy analysis methods y"+y' ^(2)=0 with initial condition v'(0)=2

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Q: a) z=-3x y² + sen(x²y) 2x c) z=-In (x y³) e) z = x²ln(2x³y) b) w=2xz-3e²xy d) z=2e²y sen(x) f) z=…

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Q: /16–y² /32–2²-y² n[L 2² + y* + z®)dzdzdy in nvert 1²+y² •1/2 4/2 -/2 Jo п/2 " T p* sin ódpdődý •4/2…

A: from the integral limits are as  follows 0 ≤ x ≤ 16-y2 0 ≤ y ≤ 4  x2+y2 ≤ z ≤ 32-x2-y2

Q: If y(t) solves the IVP dy = y2021 y2019 y(2021)= -2019, dt then lim y(t) is: t- 00 Oa. 1 O b. 00 O.O…

A: Given differential equation is dydt=y2021-y2019.       ........1 It is an autonomous differential…

Q: 3- Let µr1 = 2 in region 1, defined by 2x+3y-4z > 1, while µ2 = 5 in region 2 where %3D 2x+3y-4z <…

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Q: 1. The loop of y² = x * (4 - x) 2. у %3D 6х — х?, y = x² – 2x - 3. у %3D 2х y2 + 4x – 8 = 0 - 4. An…

A: Question 4 : Arch of y = (1/3)sin(x/3) First find out intersection points :  y = 0 (1/3)sin(x/3) = 0…

Q: 2y" +y – 4y = 0, y(0) = 0, y(0) =1

A:

Q: 2. Given y' = x² + y . With y=-1 when x=0. %3D Calculate y(0.4) and y(0.6) using modified Euler…

A: The given problem is to find the values of y(0.4) and y(0.6) using modified Euler's method for given…

Q: 4. An imaginary ant is walking on an imaginary cartesian plane so that at any point (x, y) it moves…

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Q: 6y" – 5y' + y = 0, y(0) = 4, y'(0) = 0

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Q: 23. lim Vx2 + y² In(x² + y²) (xy)→(0,0)

A: This question is related to limit in two variables.

Q: 2t-4 0st<2 (D2 - 1)y = t22 y(0)=0, y'(0)=1 Find L{y} L (1) = 1 + - - 2+ 4 2e 2s 2e-2s %3D | L (y) =…

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Q: -5) as golve: x'= -3x + 3y +z -1 (**) x-sy-32 +7 2'=-3x + 74 +32-7 =) i) Does (**) have a solution…

A: As per norms, we will be solving only one question. If you need an answer to others then kindly…

Q: 2,2 2 (xy +x)dx = (x'y+x+y+1)dy O In(x² – 1) =y² – 2y + 4ln|c(y +1)| In(x² +1) =y² - 2y +…

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Q: 2t – 4 0st<2 (D² – 1)y = [2 t 2 y(0)=0, y'(O)=1 Find L{y} O L 1) = + -1) 2e-2s +. s(s² -1) 4 2e s2…

A: To solve given question first we take Laplace transform of both sides and solve.

Q: 2. If the Wronskian of y1 and y2 is e2" (x² + 5) and y1 = e2", find y2. %3D

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Q: 2t – 2 t2- 1, Let r(t) = - î - tan (t) ĵ+ In(2t) k. %3D (a) Determine the domain of r. (b) Compute…

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Q: 4y" – y = 0, У-2) %3D 1, у(-2) %3D -1

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Q: 2х + 3 dx Using partial fractions, the integral x(x² + 2x + 5) – (x² + 2x + 5) Вх + С + +b' ax? can…

A:

Q: 2. Consider the ODE 2 3 y' +-y = 3+1 With the initial condition that y=1 when x = 1. a. Show that…

A: Given: Let us consider the given ODE, yι+2xy=3x3+1;y1=1 a) whether ux=e∫2xdx =x2 ∴ux=x2 Promptly,…

Q: 1-6 Use an appropriate form of the chain rule to find dz/dt. 1. z = 3x²y*; x = r^, y = r² 2. z =…

A:

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.