y' + 4y = e^(4t) %3D

Q: Find the divergence of the vector field F. F(x, y) = 4xe*i – 3x?y?j

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Q: For the given function find dy/dx. x- y' | = x + 2 y+ x2 1- x-3y-4x 3x2 + y + 2 y' 1- x + 3y - 4x y…

A: x-y3y+x2=x+2

Q: Find div F and curl F if F(x, y, z) = 11y"2°i – 17x"z1ºj – 6xy°k. - div F= curl F=

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Q: f(t) 3. Find the function f and a number a such that a + dt = 2 sin x for all x greater than zero.…

A: We can solve as follows

Q: Find the arc length of the graph of r(t) eV2li +e¬V2lj+2tk, 0<t< v2 ln 9 NOTE: Enter the exact…

A: Given problem:-

Q: Evaluate. 1 6 x dx V16 +3x2 0. V19 A) B) 2/19 -8 C) V19 -4 - 2 D) -219 +8

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Q: Find the second derivative [ f"(x)] of the given function: f(x) = eln Vx²+2 %3D (x2 + 2)) x(x² + 2)-…

A: Given problem:- Find the second derivative [f''(x)] of the given function:   f(x) = eln√(x^2+2)

Q: įy'ny dy 2e' +1 Ans. 9. 13.

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Q: Find the volume of the solid that results when the region bounded by x=y^2 and x=4y+5 is revolved…

A: Given: To obtain the volume of the solid when the region bounded by x=y2 and x=4y+5 is revolved…

Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j…

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Q: Find the derivative, dy/dx: y = x² In x3 ý =- 2 1-4 ln x x³ In? x 3. ý = -2 In x – 2x | y = --(- 3…

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Q: d Find [r(t) · u(t)] and [r(t) x u(t)] in two different ways. dt dt r(t) = ti + 2t2j + t³k, u(t) =…

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Q: In an extensive study of cost functions for 40 firms in Great Britain, it was found that if a is the…

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Q: Find div F and curl F if F(x, y, z) = 4y®z°i – 11a°z°j – 5xy'k. div F= curl F=

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Q: ||r'(t) × r"(t)|| Use the formula k(t) to find k(t). r(t) = e"i+ e¬'j K(t)

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Q: Find the first three non-zero terms of the Taylor expansion for the given function and given value…

A: The Taylor series;  fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+..... Where, center at x=a.   Given:…

Q: sin 201/1+ 2 sin 0/cos? 0 (sec² 0 – 1) d0 1. |

A: To find the following antiderivative.∫sin 2θ1+2 sin θcos2 θ sec2 θ-1 dθ

Q: Find the dimensions of a rectangle with perimeter 1000 metres so that the area of the rectangle is a…

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Q: Find both first partial derivatives. z = 15XVY 15xVy %3D dz az

A: We need to find partial derivative.

Q: Find the volume of the solid obtained by rotating about the x-axis the region under the curve y=…

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Q: Consider f(x) = (5x + 11)2022, find: i. f'(x) ii. f"(x) iii. f''(x) iv. fiv (x) v. f°(x)

A: Given, f(x)=5x+112022

Q: ( (am (39) + ce (39) sin (39) - ar (3) dy 3y)) sin² (3y) – tan² (3y)|

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Q: Solve for the general solution of the non-homogenous linear differential equation using the method…

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Q: Find the eigenvalues of the matrix and determine whether there is a sufficient number to guarantee…

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Q: Use the Fundamental Theorem of Calculus to find the "area under the curve" of f(x) = 8x + 7 %3D…

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Q: about the line, x- | (E'1) puo (!!)'(0) squiad %3D V= T RG) 3-X y= 2x+1 Idy 3 - 23. x- V= T 29 12

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Q: Given f(x, y) = (3x – a²)(2y – y²). (a) Find all the critical points of the function. (b) Classify…

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Q: Determine the area of the region between the x-axis and the graph of the curv -1 from x- 0 to x- 4.…

A: Area bounded by curves :   If f(x) and g(x) are two continuous function on a,b and f(x)≥g(x) on a,b…

Q: Evaluate the following definite integrals. dr 5. ? +3

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Q: Find all the first and second partial derivatives of the function f(r, y) = x°y – 3y“. %3D

A: Given :f(x,y)=x2y-3y4To find : All the first and second partial derivatives of the function

Q: Represent the line segment from P to Q by a vector-valued function. (P corresponds tot = 0. Q…

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Q: In +1- 2 dt, if we let V Vt+1-2, then dt is equal to t+1– 2, then dt is equal to A) None 4x³dx ©…

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Q: Find div F and curl F if F(x, y, z) = 13y'2*i – 11x°z®j – 7xy°k. %3D div F= 0 curl F=|(-35 z y³ + 99…

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Q: The total revenue, thousands of dollars, for selling g thousand Framits is given by (a) Find all…

A: Note: According to our expert guidelines only first three subparts are to be answered kindly repost…

Q: ind [r(t) · u(t)] and Ir(t) x u(t)] in two different ways. dt r(t) = ti + 5t2j + t³k, u(t) = tk (a)…

A: Solving

Q: Find V x (V x F) if F(x, y, z) = 9xyj+ 6xyz k. V × (V × F) =

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Q: Given the function + y-4, find y'. Oy = Oy =

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Q: The most conveneient way to evaluate x2- by substitution is to let Vx2- 4 =y A True B) False

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Q: Find the area of the quadrilateral lot shown in the figure below to the nearest square foot. 130 ft…

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Q: Find the series' radius of convergence. n! Σ 5-10 - 15...- -5n n= 1

A: We have to find the radius of convergence.

Q: Find the general solution of y'' - 2y' - 8y = 24(x2+1)e4x by using VARIATION OF PARAMETERS

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Q: (x^2+y^2-3)dx-2xydy=0 Prove the given DE is exact, and find general solution

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Q: Is the mathematical statement correct. If f(x)=f(-x), then f’(x)=f’(-x). Explain why

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Q: Complete the table. (Use C for the constant of integration.) Original Integral Rewrite Integrate…

A: We can evaluate the given integral by using the following formula.

Q: Find V x (V × F) if F(x, y, z) = 9xyj+ 6xyz k. V x (V × F)

A: WS have to solve the vector

Q: Given the linear differential equation: y'' - y = cos(x) - 5sin(2x) Find the general solution…

A: Solving

Q: X= 6 The area enclosed by the curves Y= and y= 2x from x= 1 to x= e is 2) e +1 O 3) +1 O 4) 2-2

A: Given query is to find the area enclosed by the curves.

Q: 3x2+14x+13 x+4

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Q: EVALUATE EACH OF THE FOLLOWING INDEFINITE INTEGRALS. Sh dx

A: Since we are given with the multiple number of question and our guideline is solve first question…

Q: *+ 2y = te-2t, y(1) = 0 2. Solve the IVP: dt

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