S₁ y² – 3ydy 11

Q: Consider the initial-value problem y' + ey = f(x), y(0) = 1. Express the solution of the IVP for x>0…

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Q: dx 3. If 8c²xy = (x² - y2)2, find- dy

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Solve the given differential equation. All solutions should be found. dy 3x² – 2y — y³ dx 2x + 3xy²…

A: This question is related to differential equations, we will solve it using given information.

Q: (ii) Suppose z = f(x, y), where x = g(s, t), y = h(s, t), g(1,2) = 3, gs (1, 2) = −1, gt(1, 2) = 4,…

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Q: Let y = f(x), where f(x) = 7x³ + 3x. Find the differential of the function. dy = X

A: The differential of y is the derivative of the function times the differential of x,

Q: 16. True or False: (a). Every element in a cyclic group (G) is a generator of G. (b). A group (G, *)…

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Q: 3. Consider the vectors X and Y in R³ where X = -i+3j and Y = 4i - 2j + 2k. Find the unit vector…

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Q: aw C. If w=f(x,y) and x=r. cose, y=1. sing. Prove that ar 1 (dw r² 20 = fix² + fy²

A: Let's prove.

Q: 8) S dx it sinx + cos x a) in (1 + tan =) + c b) In (i - tan £) + c c) - In (1 + tan x) + o 2 d.)…

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Q: The graph of f is given below. -2.5 -2 -1.5 Why is f not differentiable at x = 0? Of is continuous…

A: Given graph of a function f.

Q: Use any method to find the derivative of the following (the results do not need to be simplified):…

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Q: Consider the vectors X and Y in R³ where X = -i+3j and Y = 4i - 2j + 2k. -Y. 3. Find the unit vector…

A: Follow the procedure given below.

Q: What is the derivative of y = sin (x³ sin (x³ – 3x)?

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Q: Determine whether the series is convergent or divergent. If it is convergent, find its sum. 9 27…

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Q: The graph of f is given below. -2.5 -2 -1,5 Why is f not differentiable at x = 1? Of is continuous…

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Q: Solve the following initial value problem using Laplace transforms. y"+2y'-3y=3e¹, y(0) = 0,…

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Q: Find the volume of the solid generated by rotating the region enclosed by y = x + 3, y = 0, x = 1,…

A: Topic = Volume

Q: Determine the area of the region enclosed by the curves y - 3x = 2 and 2x² - 4-2y = 0. Do not…

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Q: Z = 5 X 4 2 -7x+8 d²z dx2

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Q: Given a function, Based on the function, F(s) = 2s +3 s²-2s+25 a) Determine f(t). b) Based on…

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Q: Which one of the following is the gradient of the tangent line at the point (5, 1) on the graph of,…

A: To find the gradient of the tangent line of the point (5,1) on the graph of x+xy+2y2=12 Formulae…

Q: 1. Determine whether the series n=1 3n+1 ln(n+1) is convergent or divergent.

A: : since,1< ln(n+1),for n>2 so, 0<(n^2)/(((3^(n+1))*ln(n+1))<n^2/n^4=1/n^2,  since…

Q: what is y' of y=sin-1(cos x)

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Q: Q4/ Answer two from the following :- 4- Evaluate and change the order of integration in 1 = ²*xy…

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Q: The speed of sound traveling through ocean water with salinity 35 parts per thousand has been…

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Q: Find the Taylor series expansion of f(x) = ln(3-2x) about a = 1.

A: Given: f(x)=ln3-2x,a=1

Q: State the order of the given ordinary differential equation. (1-x)y" - 5xy' + 2y = cos x Determine…

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Q: Identify ALL the Indeterminate forms involved and determine the limit of: limo+ (cos(x))"

A: See the answer below

Q: 2x³ is an antiderivative of what function? y = 6x² y = -6x² X y = -2 y = X 2

A: Integrating the given function gives the antiderivative.

Q: When is a function Fan antiderivative function f? of a if F(x) is continuous for all x in the domain…

A: We know that,  if a function F( x) is called an antiderivative of a function of f( x) if      F'(x)…

Q: Q4: A conical tank with Diameter of (2 m) from the top and (5 m) height. At the bottom of the tank…

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Q: Find the solution of the given initial value problem in explicit form 1 y' = (1 - 5x)y², y(0) = 9

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Q: 3- اول ** X 2 Sin² Lys y

A: Follow the procedure given below.

Q: _z = g(x,y)=√x² +2y²

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Q: Show that the series n=0 xn cos(nx) x² +n³ + 1 defines a differentiable function g(x) for x in [-1,…

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Q: Let E be the region in the first octant enclosed by z = √√√x² + y² and z = 2. Which of the following…

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Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

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Q: L’Hopital

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Q: Find an antiderivative for each function when C = 0. a. 1 b. 2√x 1 c. ²{√x + 7/7 C. a. The…

A: Formula ∫ xn dx=(x(n+1))/(n+1) +c

Q: Given a function, Based on the function, 2s +3 F(s) = s² -2s+25 a) Determine f(t). b) Based on…

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Q: 50° 60° 70° ?

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Q: f sec¹ x dx

A: Integrate the integral sec7x .

Q: Prove that For all A ∈ A, we have 0≤ P(A) ≤ 1

A: Concept: Probability: Probability signifies the possibility of something happening. It's a…

Q: Question 2: Let E be the solid inside the surface x² + y² + z² = 10% and above the plane z = 5. (a)…

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Q: Determine the area bounded by y = x³ and y = 4x using a vertical element

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Q: ſº 5u³ – 3u³ – 9du

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Q: Solve the given differential equation by finding, as in Example 4 from Section 2.4, an appropriate…

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Q: B. 2x³ +2y-3y² = 13x Steps 1. Take the derivative of both sides with respect to x. 2. Since the left…

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Q: What is the derivative of y = 8 cos x? -16 sin x -8 sin x 8 sin x 16 sin x

A: In this question, we need to find the derivative.

Q: y²-6x²y=-9x ; y' at (1,3)

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