Q1:/ Find the general solution of non-homogenous differential equation using Variation of Parameters method y" - y'=e* cosx

Q: Find the derivative of the following using the differentiation rules. (x²-2x) (In x³-3 tan x) x√x y

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Q: The region is bounded by y = x³, y = 2x + 4 and y = -1. Then Arearegion = [*^f(x) dx + [²8(x) x +…

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Q: 2x² 3x²-5x (a)y=-

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Q: (4) Find Laplace Transform F(s) for the variable x or y in the equations a- y" +2y'-3y=32e";…

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Q: Part II f(x)=x² A. g(x)=(x-3)² f(x)=x² B. g(x)=(x+3)² p(x)=(x-3)² +5 p(x) = (x+3)² +5 f(x)=x²…

A: We need to find vertex. As per Bartleby's guidelines we can solve only one part. Please upload other…

Q: Evaluate the limit using L'Hopital's rule. Answer should be expressed as an INTEGER value, with NO…

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Q: The force on the triangular plate that is submerged in water as shown below waters surface 6m 4m is…

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Q: Consider the region on the 1st quadrant bounded by y = √4x²,x and y- axes. If the region is revolved…

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Q: 3x at the point P (2,0, -1) in the direction The directional derivative of f (x,y,z)=ln *(x,y,z);…

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Q: W=-Si ; V=1-2i, W=-3-6i , U-3V+ 2W, UV, UVW, : Given U= 4-2i ; V= 3-4i atib= (utiv)w, find a ad b.…

A: Here is the solution:

Q: The region is bounded by y = x³, y = 2x + 4 and y=-1. Then Arearegion= = ["f(x) dx + ["g(x) [*g(x)…

A: The region is bounded by y=x3, y=2x+4 and y=-1. Then Arearegion=∫abfx dx+∫bcgx, where a<b<c.To…

Q: U= at ² w + 0х2 8² w dy² where 61, 62, 63 are constants and b₁ +6₂ +63 " 8² w + = W. az² Item 8.pdf…

A: Topic:- application of partial derivatives

Q: Consider the vector-valued function In(2t + 1) sin t R(t) = î+ t t Redefine (t) such that it is…

A: we say the R(t)  is continuous at t=0  if limt→0 R→(t)= R(0)

Q: Find the area in the first quadrant bounded by f(x)=4x-x^2 and the x-axis.

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Q: 8. y = log x-1 x+1

A: Let's find second derivative of given function.

Q: Which of the following integrals represents the area enclosed by the smaller loop of the graph of r…

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Q: 2. Using your calculator, determine how many solutions the system has. Then without a calculator,…

A: This question is based on solution of Polar function.

Q: 1. If find the value of a. L²Lke + (x + 2y)dydr = 10, a

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Q: A piece of 1m wire is cut into two parts, one bent into the shape of a circle and the other into the…

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Q: Let L(z) be the linearization of f(x) = sinz+1 at the point z=. Find L(π/2). 0-1 O pi/2-1 O pi/2 + 1…

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Q: Find the solution of y" − 8y' + 16y = 0, y(0) = 1 and y'(0) = 5. y(t) = Ae4t + Be-4t y(t) = e4t+te4t…

A: The given equation is;  y''-8y'+16y=0, y(0)=1 and y'(0)=5.

Q: If the function u = 2e^u e^2u 1/2 Other: In (2² +2²¹²) then ro + you is 4

A: First we calculate partial derivative.

Q: Let R be the region bounded by the functions f(x) = 4x² + 6x and g(x) = -2x² - 6x as shown in the…

A: Given f(x)=4x2+6x, g(x)=2x2-6x Here point  intersection of f(x) and g(x) is x=-2 and x=0 Therefore…

Q: The region is bounded by y = x³, y = 2x + 4 and y = −1. The x-coordinate of the centroid of the…

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Q: A body cools from 75°C to 70°C in 2 minutes. What will additional time (in minutes) it takes to cool…

A: Topic:  Newton's Law of cooling using application of calculus

Q: x² + 8x - 9 x1 x³2x² - 5x + 6 t³7t² + 16t - 12 t4 - 4t³+ 4t² 4. lim 5. lim t-2

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Q: if the function u= ln (x^3+x^2y-y^3/x-y) then x su/sx + y su/sy is

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Q: Find the derivative 4cos4t sin4t 2cot4t -1/2 cot4t Other: of the parametrically defined curve : x(t)…

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Q: 4. If A = 3xyz²i + 2xy³j- x²yzk and p = 3x² - yz, find (a) V-A, (b) A-V4, (c) V-(Vo) at point (1,-1,…

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Q: y = (x²-2x) (In x³-3 tan x) x√x

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Q: Evaluate the following definite integrals. Note: Final answer should be expressed as a decimal, not…

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Q: find the final value for the 3 z³ +8 F(z) = = 23-22

A: Given; F(z)=Z^3+8/Z^3-Z^2 We have to find final value

Q: n! n=12n! +1 A. The limit does not exist. B. None of the choices in this list. C. The series…

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Q: The radius of convergence of the series Place) (-1)" (n!) 0 3-6-9. (3n) (2x-1)" is equal to…

A: To find the radius of convergence of the given series.

Q: x² 8. (x) tan 3x+cot 3x 9.f(x) = 2 sin 4x cos 4x =

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Q: Which of the formulas below will give the area of the region enclosed by the polar equation r = 4…

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Q: 3. f(x) = 3x-7

A: Topic:- derivatives Note :- as per our guideline if more than one question uploaded than only first…

Q: Solve the following boundary value problem using finite difference method given that…

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Q: stion 12 The power series representation of f(x) = ln(x²-1) is given by OA. None of the choices in…

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Q: The height and radius, respectively, of a cylindrical tank is 5 m and 2 m. If the tank is full of…

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Q: Complete the table of values below. Then, sketch the graph of r = 2 - 3 cos in polar coordinate…

A: Given r=2-3cosθ in the  polar coordinate system We need to find "r" for all the angles     For θ=0,…

Q: A light shines from the top of a pole 15 m high. A ball is dropped from the same height from a point…

A: solution is here

Q: x-y •SS=20₁ -dA over a square region Using the transformations u=x-y and v=x+y to evaluate xx+y with…

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Q: Select all statements which are TRUE. For statements with cross products, assume the vectors are in…

A: Let's find.

Q: The value of x for which the series OA2<x<4. OB. 2<x<3 or 3 < x≤ 4. OC2<x<3 or 3 <x<4. OD. x<2 or…

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Q: The value of x for which the series A. 2<x<3 or 3<x<4. B. x<2 or 4<x. C. 2<x<3 or 3<x ≤ 4. D. 2<x<4.…

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Q: Use the equation to name each of the characteristics listed. Make sure to use proper notation and…

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Q: Solve the following differential equations: 1 √1-3x (a) -dx + sin y cos 2y + 1 dy = 0 (b) x²y + x³…

A: I am attaching image so that you understand each and every step. Here "c" is integration constant.

Q: Find and classify all critical points of the function 3 f(x, y) = x³ + 2y - In(x³y³) Item 5.pdf

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Q: 5x+√x 3.y=(x²+1)² 4. Using y = 5x + 3x² + 1, find all the derivatives and evaluate f"(2) f(3) (-2).…

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