Use Green's Theorem to evaluate the line integral Icov for the given path. (y-x) dx + (2x - y) dy C: boundary of the region lying inside the semicircle y = 49x2 and outside the semicircle y = 25 - x²

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.…

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Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

A: Solution ) we have option 3rd  y"+ 4y = 0 Auxilliary equation  m2 + 4 = 0 m2 = -4 m = √( -4 )  m =…

Q: *T/2 10 cos(0) r dr de

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Q: Consider the following second-order differential equation. 2y" + y = 0 Find all the roots of the…

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Q: Determine whether the given set of functions is linearly independent on the interval (-∞, 00). f₁(x)…

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Q: Let f(x) = { tan^−1 ⁡(2x) if x ≥ 0, ax+b if x < 0. For which values of a and b is f(x)…

A: topic- limits and derivatives

Q: Evaluate the integral. 6 1 (x² - 1)3/2 2 (x²

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Q: Find div(F x G) = V. (F x G). F(x, y, z)= i + 7xj + 8yk G(x, y, z) = xi - yj + zk

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Q: Osaddle point none of these

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Q: Find the general solution of the given higher-order differential equation. ²y - 32y = 0 dx² X(X) 11…

A: Find the general solution of the given higher-order differential equation.

Q: What is ette-t At- ○ - In [e* O ○ ○ dx e* + C] In [e* + e* + C In [e* e*] + C -In [ee] + C

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Q: What is the domain of the reciprocal function of f(x) = 5x+1? {x € R\x2} c. b. (x=Rxs-) a. d. {x =R…

A: We can answer the question as below.

Q: Evaluate the function at the given value of the Independent variable. Simplify the results. (If an…

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Q: Find the indefinite integral by making a change of variables. 1 √ 4 + ²√2x² dx

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Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

A: This question can be solved using the concept of differential equation.

Q: A force of 400 newtons stretches a spring 3 meters. A mass of 40 kilograms is attached to the end of…

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Q: Find where the function f(x) = 3x4 − 4x3 − 12x2 + 5 is increasing and where it is decreasing.…

A: increasing and decreasing intervals of fucntion  fx=3x4 − 4x3 − 12x2 + 5

Q: Find the gradient of the function at the given point. Function g(x, y) = ye-* Vg(0,4)= Point (0,4)…

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Q: Find the Jacobian a(x, y) / a(u, v) for the indicated change of variables. 8u, y = uv x = UV a(x, y)…

A: Given,            x=uv-8u , y=uvTo find : Find the Jacobian ∂x,y∂u,v for the indicated change of…

Q: Prove the identity. cos(3x) − cos^3 x = − cos x sin^2 x − sin x sin(2x)

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Q: Determine whether the given set of functions is linearly independent on the interval (-00, 00).…

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Q: ƒ(x) = (x³ – 4x) 10

A: Solve the derivative

Q: (2xy - x + 2y - 1) dx + (8x² y² -2x + 4xy2 - x) dy = 0

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Q: Determine whether the vector field is conservative. F(x, y) = (7y - x²)i + (7x + y)j conservative…

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Q: Find the derivative of f(x)=(x2−2x)(3x+5) by first multiplying then simplify.

A: Here we have to use the concept of derivatives

Q: Solve the initial value problem by Laplace y" +4y=20 e y(0)=3, y'(0) - 12

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Q: Use Res(f(z), zo) lim (z-zo)f(z), Res (f(z), zo) = 2-20 to find the residue at each pole of the…

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Q: Find three positive numbers x, y, and z that satisfy the given conditions. The sum is 40 and P =…

A: Given that    Three positive numbers x,y and z                The sum of these numbers is 40.…

Q: The given family of functions is the general solution of the differential equation on the indicated…

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Q: Given the exponential growth function f(x) = 83(1.0275) What is the initial value of the function?…

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Q: Solve the given differential equation by undetermined coefficients. y" - y² + ²y = 2 + ex/2 y(x) =

A: The characteristic equation is            m2-m+14=0⇒4m2-4m+1=0⇒m=--4±02· 4⇒m=12,12 Now, the general…

Q: A function f(x) is said to have a removable discontinuity at x = a if: 1. f is either not defined or…

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Q: ind the equation of the line tangent to the curve 3x² + 16y² = 192 at the point Mx + K. P= (-4, 3)…

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Q: improper iterat 1/x3 y dy dx

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Q: Please

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Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

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Q: Find the area between the curves. x = -5, x=2, y = 2x² +5, y = 0 The area between the curves is…

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Q: Evaluate the integral. (Use C for the constant of integration.) s¯¹(x) dx COS

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Q: 49-2 sin(8) = Video Example 4 EXAMPLE 1 SOLUTION Evaluate |v √49-x² x² Let x = 7 sin(e), where -7/2…

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Q: Tutorial Exercise Consider the differential equation x²6xy +10y=0; x², x5, (0,00). Verify that the…

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Q: 8) How many solutions does the equation a. 0 b. 1 X+5 x-3 IX 1 || 4 x²-3x C. 2 d. 3 have?

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Q: Consider the function on the interval (0, 27). f(x) = 1/2/20 + COS X (a) Find the open intervals on…

A: topic- Relative extrema of a function.

Q: Calculate given the following functions. O a. O b. O C. дz Əv O d. дz ὃν дz əv дz Əv дz Əv || Z = 2x…

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Q: | (8z + 4z³ - 6z²) dz? O 16z²+z4-2z³ + C O4z²+z4-22³ + C 16z²+z4+ 2z³ + C O 42² +224 + 2z³ + C

A: Solution: ∫8z+4z3-6z2dzApply the sum rule=∫8zdz +∫4z3dz -∫6z2dz

Q: f(x) = 2x²-4x x²+1

A: Given :fx=2x2-4xx2+1

Q: Use Simpson's 1/3 rule with (n₁ = 2), and Simpson's 3/8 rule with (n₂ = 3) to estimate tan-¹(2).…

A: We have to estimate the given function.

Q: -20 -19 -18 -17 -16 -15 -14-15-12-11-10-9-8-7-6-5-4-3-2 Find an equation for the graph above.

A: NOTE: Refresh your page if you can't see any equations. .

Q: 6) Identify the vertical and horizontal asymptotes of (x)= x-4 - 2x+17 b. vertical-x- 4, horizontal:…

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Q: Determine whether the given set of functions is linearly independent on the interval (-∞0,00). f₁(x)…

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Q: We have verified that x² and x are linearly independent solutions of the following second-order,…

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