Determine whether the vector field F(x, y) = 5y² (yi+2xj) is conservative. F is not conservative F is conservative

Q: Use the Fourier sine transform to solve the following BVP with 0 0 10₂4+02=0, მყ2 u(0, y) = 0, u(π,…

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Q: Find the solution of the given differential equation. dx 1 y²-6y+13 dy = 0 Express your answer…

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Q: 14. Evaluate f at its critical point(s). 15. Evaluate f at the endpoints of the given interval. 16.…

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Q: 7. Evaluate I = S ads, where S is the part of the plane x+y+z = a lying in the first octant.

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Q: Answer the following questions for the function f(x)=x√√x² +9 defined on the interval -7 ≤ x ≤ 4.…

A: Concept: Concavity: Assume that f(x) is differentiable on interval I. If f′(x) is growing, the f(x)…

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Q: For which of the following infinite series does the Ratio Test fail? IM8 IM8 k=0 k 5k そそ n=1 (n +…

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Q: What is the horizontal distance from point E to the Vertical Axis? feet

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Q: Given the demand function D(p) = √300-2p. Find the Elasticity of Demand at a price of $14 0 X

A: We can find elasticity of demand.

Q: Find an equation of the tangent line to the graph of the function at the given point. y = 8x…

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Q: xydx + (x^2+y2)dy = 0 Prove that it is a Homogenous DE using homegeneity test (degree n)and solve…

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Q: y' = CSC x y cotx

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Q: If the following equality is known to be true: -Ax + B x²2x-3 5 dx = -= √, ²2²3 - 2²/₁1 x - x + What…

A: Given data:- ∫-Ax+Bx2-2x-3dx=∫2x-3-5x+1dx

Q: Let R be the solid enclosed by the surfaces z = 3x² + y² and z = 8 – x² - y². Fill in the missing…

A: To find the missing limits of integration.

Q: Evaluate O O In 9 3 2 - In 2 In 2 x² 2 O tan¹ (2) tan¹(1) O ln 2 0 1 3 9 dx. x³ + 1 -

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Q: √64-² S.S. - In (x² + y² + 1) dx dy = ₁₂ dr dr de

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Q: Explain why if a runner completes a 6.2-mi race in 33 min, then he must have been running at exactly…

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Q: 6)    State whether the series converges absolutely, conditionally, or not at all. ∞ n = 1 (−1)n +…

A: The given series is ∑n=1∞(-1)n+1n+9

Q: 2. Let f(x) = 2x²-3x+1 ,x 0.5 Determine constants A and B such that is continuous for all values of…

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Q: Find r'(t). NOTE: Enter your answer in terms of i, j, and k. r'(t) r(t) = (tan−¹(5t))i+t cos(t)j —…

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Q: Solve: y" + 4y = x² + ex Yc=C1+C2_ Type the letter corresponding to your answer. Yp=A A_____ B с = A…

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Q: Evaluate O |x + 1/² |x - 21³ O 3 ln x²-x2 + C In In In O In x+7 x²-x-2 ·S B +C |x+2/8/3 |x-1|5/3 |x…

A: This question can be solved using the concept of partial fraction.

Q: Given the following differential equation: y' − 2y = (e^3x)/((e^x) + 1) and the following boundary…

A: Given the following differential equation: y' − 2y = (e^3x)/((e^x) + 1)

Q: The decay equation for a radioactive substance is known to be y = y₀e⁽⁻.⁰⁵⁴⁺), t in days. About how…

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Q: Solve the differential equation y'=1+5y subject to the initial condition y(0)=1. From your solution,…

A: Here we have to solve the differential equation.

Q: In each part, use the given information to find A. (7A)-1 (b) (7A) -3 [] -2 = (d) (/+2A)-! = 2 4 5

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Q: Find the area of the inner loop of the limacon given by r = 1+2sin 0.

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Q: the power series ∞ (7-2x)" Consider f(x) = Σ function. 6n n=1 as a a. Find the interval of…

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Q: Q4) A- Graph the following functions and determine (domain, range): (1) y=sin/x/ (2) y=/x²-2/ (1) y…

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Q: A botanist is studying the development of a bamboo plant. She started keeping a log of its growth 25…

A: Total time= 25 weeks Given that the plant has grown an average of 35 inch each week.  So the plant…

Q: For this week's discussion, you are asked to generate a continuous and differentiable function f(z)…

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Q: For the function f(x)=ln(1−5x)​, find the Taylor polynomials of orders​ 0, 1,​ 2, and 3 generated by…

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Q: Let r(t) = t²i + t cos(πt)j + sin(ät) k, find ſª r(t) dt.

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Q: Evaluate the following integral. 12 S 0 4 log 13 (x + X + 1 1) -dx

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Q: 5. Use the definition of a Maclaurin Series to express f(2) = as a Power Series. Give the 8th degree…

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Q: Find the slope of the tangent line to the curve 3 - 2x² + xy + y² I at the point (4, 1). - 27

A: This question is related to slope of line, we will solve it using given information.

Q: Consider the following function. f(x)=√x-9, x> 9 What is the domain of f? (Enter your answer using…

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Q: Evaluate the following integral using trigonometric substitution. 7/2 1 0 dx 2 (4x²+1) ² What…

A: I have stated the used formulas in the solution

Q: -0.001t² +0.6t, Suppose that in a memory experiment the rate of memorizing is given by M'(t) = where…

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Q: Find the exact arc length of the curve r = e from 0 = ln 2 to 0 = ln 8.

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Q: Which of the following functions are solutions of the differential equation y" - xy + y = 0? Oy=0…

A: It is easy to check through the given options.

Q: Question Find the linear approximation L(x) of the function f(x) = -5x³ - 5x²-3x - 1 at a = -4.…

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Q: Suppose that f(x) is a continuous function on the interval [0, π]. If f(x)=(sin x)² for 0<x<, then…

A: Since the f(x) is continuous function in [0, π], therefore the value of function at x = 0 must equal…

Q: 1 1+exte -X dx

A: Yo evaluate the integral.

Q: Consider the function f(x) = 3x + 8x-1. For this function there are four important intervals: (-∞o,…

A: Use differentiation for finding A and B and C

Q: A license plate must contain 2 numerical digits followed by 2 letters. If the first digit cannot be…

A: Given 1. A license plate must contain 2 numerical digits followed by 2 letters. 2. the first digit…

Q: Use substitution method to evaluate the definite integral fore dx

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Q: Find an equation of the plane containing the point P (1, -7,1) and the line r (t ) = .

A: Given: The point P (1, -7,1) and the line r (t ) = &lt;3 − 2t, 4t, 7&gt; . So,             x = 3 −…

Q: For the function f(x) = 3x² −x³ – 4 where −3 ≤ x ≤ 3, complete the following. 1. Find f' and f". 2.…

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Q: Express the equation in logarithmic form: (a) 45 = 1024 is equivalent to log4 A = B. A = and B = (b)…

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