7. y = tan ex + etanāx

Q: How to solve the following ordinary differential equation (ODE) xy' – 2y + y² = x“.

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Q: Prove that 3x +8 Viv = dr dy: %3D where R [-1,1] x [0, 2).

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Q: Consider f(x)=ax+xln⁡(bx) for a>0a>0, b>1b>1, and x>1x>1. Find f′(x)f′(x): f′(x)=f′(x)= ------- Bas...

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Q: 5xyz dv, where T is the solid tetrahedron with vertices (0, 0, 0), (1, 0, 0), (1, 1, 0), and (1, 0, ...

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Q: SHOW YOUR SOLUTIONS. I. Eliminate the arbitrary constants. 5. (x – a)² + y² = a²

A: Given :   (x-a)2+y2=a2

Q: What is the integrating factor for the differential equation?

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Q: 1. y = ax? + 2be2x

A: Since you have posted multiple questions in this question which are not interlinked so I have solved...

Q: ( 2x-sy+12) dx +(7x-4y+15)dy = o 2,

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Q: Evaluate the following integrals |(6V - x-3)°dx

A: The integration of the integral is (6√x - x-3)2

Q: (2 cos 3w – sec 3w tan 3w)dw

A:

Q: Question 3 If f(x)=cos x, then f"(x)= O cos X

A: f(x)=cosx,f'(x)=ddxcosx=-sinxf''(x)=ddx-sinx          =-ddxsinx          =-cosx  

Q: Determine the value of the given integral given the equation presented below. Answers should be expr...

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Q: Find the volume of the pyramid with base in the plane z = -1 and sides formed by the three planes y ...

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Q: 4. y = xcoSx

A: First we take log both sides and then differentiate both sides with respect to x.

Q: a) [ „J: Evaluate the integral (4x + 1) In x dx b) ' . Evaluate the integral fou 6 tan' x sec* x dx ...

A: a) Given:       ∫4x+1ln x dx Integrate by parts: ∫fg'=fg-∫f'g where f=ln x , g'=4x+1           f'=1x...

Q: 4. Consider the surface S parametrized by R(u, v) = (uv, sin u, cos v). Find an equation for %3D the...

A: The given curve S is parametrized by: R→(u,v)=uv,sin u,cos v Now, to find the equation of the tangen...

Q: Determine the maximum and minimum values ​​of the function f(x, y) = 2 +x+ 3y, in the region  x ≥ 0...

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Q: S 12x²Vx3 + 7dx

A: This question can be solved using the concept of integration by substitution.

Q: S sin 8x sin x dx O - 0. 02 O - 0. 01 O 0.02 0.01 O O O

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Q: 8. Using (4.6), find the polynomial P2(x) that interpolates the following data. In each case, simpli...

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Q: Find the derivatives of the following functions: 1. y = 2x3 + 6x 2. y = 7x* - 3x? 3. y = (3x +1)(2x ...

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Q: The position of a car traveling along a highway is given by the function s(t) = - + 31² + 20t – 3 wh...

A: Given:     Function st=-2t33+3t2+20t-3    where t≥0 Velocity vt=ddt-2t33+3t2+20t-3                  ...

Q: 221 writc a formnla for the function y =f cx) whose is shown fig: 2.

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Q: 12x e-y with x 20 and an initia. Solve the initial value problem condition y(0) = 1.

A: Topic = Differential eqaution

Q: :6. Bet“ dt.

A: (6). Given: I=∫t3et4dt   ...1   We know that; ∫eax+bdx=1aeax+b+C   Note; As per Bartleby guidelines ...

Q: 2.) State one of the two formulas for finding the derivative of a function f(x) that uses limits. Us...

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Q: From Rogawski ET 2e section 8.1, exercise 9. Calculate the arc length of y = - x - In x over the int...

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Q: (7) Use the definition of convergence for a series to prove that 2 n2 + 4n + 3 n=0 converges. Find t...

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. 1 x = -(y2 + 2)3...

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Q: tan x[cot x – cos x]dx |

A: Topic:- integration and trigonometry

Q: Assume that all the given functions have continuous second-order partial derivatives. If z = f(x, y)...

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Q: Differentiate: -X=COS y O a. -sin y O b. -1/sin y O c. cSc y O d. secy

A: Topic:- derivative

Q: 18) rind fue indefinite inpagrel by ma uing tue Subs titel fion x=2Seco. af -de

A: The detailed solution is given below Thank you 

Q: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley ...

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Q: Question Find (f-)'(a) for f(x) = Vx + 5 when a = 2. (Enter an exact answer.) Provide your answer be...

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Q: 25 Given the function f(x) = x°+ x° + x*, find all x-values where f has an inflection point.

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Q: 7 Type equation here.

A: topic - indefinite integral

Q: X sin? - cos 2 2. -dx 2

A: Yes. This problem can be solved using Wallis formula.

Q: (a) f(x) = (3x² – 1)/T +x/4 (b) y(x) = r-1 r³+2 (c) g(t) = [(t³ + 4)(t² – 1)]/

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Q: 2. Matching type: Match the functions in Column A with their corresponding antideriva- tives in Colu...

A: so in column A is given the derivative of column B so we derivate the column B a F(x) = 3x3 - x now ...

Q: Show that w is in span(B) and find the coordinates of w with respect to B. B = 6.

A: Linear Algebra

Q: Lesson 13 Find the derivative of the following functions. Show your solution. 1. y = x' cos x 2. y s...

A: This can be solved as follows:

Q: E Find the differental equationof the family of plane curves described. Dran at least three members ...

A: Solved below

Q: INTEGRATE THE FOLLOWING (use integration techniques) -2y dy 2. Sy'e-24 dy

A: topic- indefinite integral

Q: Question 6 P Consider a room in the shape of a 4 m cube, 4 meters on each side. A bug at point P wan...

A: Given problem:-

Q: w = x18yz14 + sin(yz)

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Q: Identify u and dv for finding the integral using integration by parts. Do not integrate. 489x хе dx ...

A: ∫xe489x dxBy using integration by partsu=x, v=e489x

Q: 6. S Ve3x + e4x dx

A: 6.∫e3x+e4x3 dx∫e3x+e4x13dx

Q: Work Problems a) Evaluate the integral (4x + 1) ln x dx b) Evaluate the integral fou | 6 tan" x sec“...

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Q: • TT 2. sin? cos' –dx 2

A: