Solve the general solution of DE: y" -5y' + 4y = 3e6r O y = cje* + c2er + ner 10 y = cje* + czet* + efr O y = cje + cze* + 100 3. O y = cje* + c2ze* + 10 3

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Q: Use the formula «(t) = F () ×F (51 to find k(t). ||r(t)||* r(t) = t²i+t°j K(t) = %3D

A: We have t find κ(t) for the given vector r(t) = t2i + t5j The given formula is κ(t) =…

Q: Exercises Distinct Real Roots of Auxiliary Equ d the general solution 1. (D² – 9)y = 0 5. (D² – 1)y…

A: Topic:- application of integration

Q: Find the limit. NOTE: Enter the answer using round brackets. t? +9 1 lim t+oo 3t2 + 4' 6t = (?, ?)

A: 1/infinity=0 is used

Q: 5. y = (x+7)(5x- 2)

A: Given : y=(x+7)(5x-2)   To Find : Derivative of the given function.

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Q: 1. Find the particular solution of the DE y" -11y' + 24y = 0 subject to the boundary conditions y…

A: The differential equation can be solved as follows:

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Q: Find div F and curl F if F(x, y, z) = 7e*Y i – 6 cos yj+ 10 sin? z k. - div F= curl F=

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Q: e2y dy Solve using algebraic substitution Tey-i

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Q: dy + 2ху dx %3D

A: integrating factor method.

Q: Find the radius of convergence, R, of the series. Σ n = 1 R = Find the interval, I, of convergence…

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Q: ||r(t) × r"(t)|| ||r(t)||* Use the formula k(t) to find k(t). r(t) = ti + t°j

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Q: The area enclosed by the curves y = x + 2 and x is . y = 7 + 5x %3D - .... 1) 36 2) 120 3) 34 4) 118…

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Q: Find curl (4zi+ 5xj+8yk). curl(4zi+ 5xj+ 8y k) = ( i )i + ( i )j+( i %3D

A: As we know that; The expression for the curl of the vector point function F→=F1i+F2j+F3k is; curl…

Q: Find curl(Sz i+6x j + 7y k), curl(Sz i+ 6x j + 7y k) =( i+(

A: This question van be solved using the concept of curl F.

Q: Evaluate the double integral. 7x sin y'dA; Ris the region that is bounded by y = x², y = -x', and y…

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Q: A function f has the following graph: 4- -3 -2 1- -2 -1 5. 6. 8. -1- -2- Which of the following is…

A: Graph of the function is given, we have to discuss about continuous of the function

Q: Describe the graph of the equation. r = 7 sin 6t i – 7 cos 6t j O It is a circle of radius 6 in the…

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Q: b. Vr4 – 2.x² + 1 dx

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Q: Barbara put P100 into banks savings account. The account accrues a 9% interest rate compounded…

A: Given: Amount =P100 . Rate of interest= 9%  Time n= 12 years

Q: Evaluate the indefinite integral. (Remember 26 dz ,7 z' + 2

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Q: ind the average value of the function g(t) = e' over the interval [0, 8]. ound your answer to one…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Let F(t) = < 5t + 5, t - 2t, 2 In < 5t' + 5,f – t, a. Determine the coordinates of the point on the…

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Q: Definite Integral. 2.) S x²(2x³ + 1)*dx 4.) x?e*dx 6.) f- xp:

A: To integrate.

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Q: Given the function f(x) = x² and the closed interval [0, 1], which of the following is a value of c…

A: Given query is to find the value of c.

Q: Given the function: x² –4 if x + 2 f(æ) = { k, 2-x if x = 2 What should be the value of k so that…

A: We have to find value of K

Q: A publisher for a promising new novel figures fixed costs (overhead, advances, promotion, copy…

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Q: Find the exact area under the curve between the indicated values of x. y =x2 - 6x + 9; between x= 2…

A: Solution: ∫24(x2-6x+9)dx

Q: A general solution of the differential equation d3y/dx3-3d2y/dx2+4=0

A: The given differential equation,        d3ydx3-3d2ydx2+4=0

Q: (a) x = 0: dy/dt (b) x = 2: dy/dt (c) z = 3: dy/dt

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Q: Solve the problem. Let D be the region bounded below by the cone z-x2+y2 and above by the sphere z-…

A: Given

Q: On what intervals is the function f(x) = continuous? x(x - 1)(x- 2) 1. (-00,0) 2. (0,1) 3. (1,2) 4.…

A: First draw the graph Uasing limits and the check the countinity of this function

Q: L 3a da = 65 Select one: O True O False 2Vada = 104/3 %3D Select one: O True O False L(z +4)(z +3)dz…

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Q: cx2 + 8x if x < 3 Let f(x) = 1 x3- cx if x 2 3. For what value of the constant c is the function f…

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Q: Find the magnitude and direction angle of the given vector. 5. u = (-10, 24) 6. u = (-5, -12) %3D n…

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Q: ||r(t) × r" (t)|| ||r(t)|* Use the formula k(t) to find k(t). 3 r(t) = 7 cos(4t)i+ 7 sin(4t)j+ 5tk…

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Q: 2. dy dx

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Q: Find curl (2z i + 3x j + 5y k). curl (2z i + 3x j + 5y k) (i )i + ( i j+ ( i )k

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Q: Find the indefinite integral. (Use c for the constant of integration.) (4t³i + 4tj – 6/ik) dt

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Q: How many arbitrary constants will be there n the general solution of a second order differential…

A: The number of arbitrary constants in the general solution of a differential equation is equal to the…

Q: 4y" – 4y' + y = e"/2/1 – x².

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise.…

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise p…

A: As we know that; The Green's theorem; ∫CPdx+Qdy=∫∫D∂Q∂x-∂P∂ydA   Given: I=∫C3xy dx+6xy dy And C:…

Q: Using appropriate substitution 9x2 – 4 dx X is equal to

A: