By using substitution of x-e' and t = ln(x), find the general solution of the differential equation.

Q: b- dy +2y=0; y=1 at t=0, y(0)=1 dt

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Q: If u = ₁+₂y+z, where a₁, A2, A3 al constants and J²u J²u J²u น a +a+a = 1. Show that + + = U. მ2 მყ2…

A: This question is based on Partial diffrentiation.

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

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

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: The value of the integral in terms of u is? (a). 2u³ + 6u + Arctanu + C (c). 2u³-21n|u³+1| + C dx…

A: To evaluate: ∫dxx3+x Let I = ∫dxx3+x Assuming x=u6⇒dx = 6u5du

Q: d'y dx2 -sec³t -csc³t Find a. O b. O c. sec³t Od. csc³t Oe. in terms of t of x = sint, y = cost none…

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Q: Evaluate the following double integral over the given region R. 2 ln(x + 1) (x+1)y Use integration…

A: The objective of the question is evaluate the definite double integral.

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: Use the shell method to find the volume of the solids generated by revolving the shaded region about…

A: Volume of solid revolving about x axis  between curves h(x) and f(x) is given by

Q: create 2 sample word problems of chain rule

A: 1) Differentiate cos(sin(ax)) by using chain rule   d/dx { cos(sin(ax)) }  =  - sin(sin(ax)) * {…

Q: Let f (a, b, c) = cos (ab) + sin (b) + c where f ¹ ((1/5,²)) af 1 T Evaluate да 23 π T√3 12 3 Option…

A: I am attaching image so that you understand each and every step.

Q: In solving for the area bounded by y = x, y = 2x and x + y = 6 using a vertical element, the total…

A: We have to find value of area AL

Q: 5. Evaluate the following integrals: 'T (a) cos(x) dx dy 4y (b) ₁. [ [² e-1²-y² dy dx (Hint: Use…

A: (a) ∫0π4∫4yπ cos(x)dxdy=∫0π4sin(x)4yπ…

Q: Given the function f(x,y)=x³-5x² + 4xy-y²-16x - 10. Which ONE of the following statements is TRUE?

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Q: 7. Evaluate * (D5 – 3D¹ + 8D³ + 16D² – 9D – 13)y = 0 y = (C₁+C₂x)e¯x + Сze* +C₁е²x cos3x +C5e²x…

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Q: Choose among the following suitable to define the given integrations: * f(x + 1) sinx dx Not…

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Q: dx Consider S= using rationalizing substitution. x1/2 + x2/3 Find the integrand in terms of z. A…

A: find out the integrand in terms of z.

Q: For the given cost function C(z) = 250√ + find 8000 a) The cost at the production level 1000 b) The…

A: Cost

Q: y = (x²-2x) (In x³-3 tan x) x√x

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Q: 5. f(x) = e³x-5 6.f(x) = (1 + cos x)8

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Q: The integral can be rewritten as 6u³ (a). Su + 1 di du 6u4 (c). √ ₁² + 1 du dx ³√x + √x S 6u² (b). √…

A: Given :∫dxx3+x

Q: The graph of r = -2+3 cos is symmetric with respect to the O x-axis and origin origin only

A: given r=-2+3cos∅   it is the equation of limacon.

Q: 4. x = 3 + 4 sine, y = 3cos0 - 4

A: Given: x=3+4sinθ, y=3cosθ-4 dxdθ=ddθ3+4sinθ = 4cosθ dydθ=ddθ3cosθ-4 = -3sinθ

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

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Q: Use Lagrange multipliers to find the critical points and the relative extrema. f(x,y) = 4x² + 2y² +…

A: We have to find  the critical points and the relative extrema.

Q: x² In solving for the antiderivative of f(x)= √√4-x² using trigonometric substitution, f(x) dx is…

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Q: Suppose that x = 2 tan 8. What is sec e equal to in terms of x? √4+x² 2 √4+x² X Option 1 Option 2…

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Q: (D^5-3D^4+8D^3+16D^2-9D-13)y=0 nonhomogeneous undetermined coefficients

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Q: Find dy dx : y = arctan 2+1 x-1 at x = 1

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Q: 2. y = (x + 1)2 and y = -x + 1

A: Topic:- application of integration Note:- as per our guideline if more than one question uploaded…

Q: -3x² 2(T T + 10 25)

A: Follow the procedure given below.

Q: The area between the curves f(x) = x and g(x)= x^2 on interval [0.2] * 02 Me: wow I finally…

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Q: II. INDETERMINATE FORMS COS X X 5. lim x →∞0

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Q: The cylindrical shell method is to be used to compute for the volume of the solid generated by…

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Q: In evaluating 5 3 Add your answer dx is same as evaluating lim (In(f(x))). Determine the value of…

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Q: 1.ƒ(x) = 4x³ – 7x² + 2x − 8 -

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Q: The formula for solving for the area in the first quadrant bounded by y = x², the circle x² + y² =…

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Q: What is y2 = 3x in polar form? r = 3 sin 0 sin 0 O Option 4 r = 3 csc 0 cote Option 2 r = 3 sin 0 -…

A: Given y2=3xTo find polar form:

Q: Find and classify all critical points of the function f(x, y) = x³ + 2y4 - In(x³y³)

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Q: Consider the series Σ(-1)^ 2³ Which ONE of the following statements is CORRECT? n=1 3" OA. The…

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Q: For a cyclic group of order 420, the number of generators are, (a) 66 (b) 76 (c) 86 (d) 96

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Q: Set up the integral representing the area of the region between the curves * = :-2, x = 3, y=x²-3,…

A: We have to find value of area of shaded Region.

Q: Find lim 1-0 does not exist -1/2 Ο Οι Ο 1/2 O O Ο Ο Ο Ο Ο Ο O O O e* - r -1 Other: Δ

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Q: Using √√x + 1 √x-1 express the final answer in terms of X. Substitution Rationalizing dx = y² + 4y+…

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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: Find: y = arctan = 1 O a. none of these O b. 0 с. O d. 177 O e.

A: Given;  y=tan-1[(x+1)/(x-1)] at x=1.

Q: Find the Critical points of the ff equation and Determine the Maximum and Minimum. - 2. y= 4x -432x…

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Q: Evaluate S dx √x² +25

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Q: IV.Sketch the ff. curves: Find all its properties. X 1. y= In x

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