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Q: A rectangle is inscribed inside the curve y = √9 -x in the first quadrant so that the base is on the…

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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

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Q: The indicated function y(x) is a solution of the given differential equation. Use reduction of order…

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Q: The answer for x is correct but the answer for dy is wrong.

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

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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: Solve the differential equation by variation of parameters. y" + 2y' + y = e-t In(t) y(t) =

A: The DE is given as , y''+2y'+y=e-tlnt find the solution by variation of parameters.

Q: Find curl(curl F) = x (V x F). F(x, y, z) = 4x³yzi + yj + 4zk

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Q: For y=x²-9x+8, find dy, given x = 1 and Ax = -0.1. dy = (Simplify your answer.) 5 2d

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Q: Consider the following second-order differential equation. 3y" + 2y' + y = 0 Find all the roots of…

A: We have to find the general solution.

Q: Find a unit normal vector to the surface at the given point. [Hint: normalize the gradient vector…

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Q: Use polar coordinates to describe the region shown. y L -6 -4 -2 6 OR ((r, e): 0 ≤rs 6 cos(38), 0 ≤…

A: We need to find equation of polar curve.

Q: Solve the differential equation by variation of parameters. y" + 3y + 2y = 2+ e* Step 1 We are given…

A: y''+2y'+2y=12+ex

Q: Let - fot² Find the average value of f on the interval [0, 1]. f(x) = dt.

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Q: Find all x-intercepts and y-intercepts of the graph of the function. 2 f(x)=1³-1²-9x+9 If there is…

A: We will solve.

Q: 5 Find the equations to both lines through the point (2,-2) that are tangent to the parabola y = x²…

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Q: Find the gradient of the function at the given point. w = 5x²y-7yz+z², (1, 1, -2) O 15i+ 26j+ 11k O…

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Q: ¡ (ew - 3) dw? O ew - 3w+C O - ew + 3W + C O -ew - 3W + C O ew - 3+ C

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Q: Sketch the region R of integration and switch the order of integration. 81-x2 LV²²- -10 O -10 f(x,…

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Q: Consider the following second-order differential equation. 5y" + y = 0 Find all the roots of the…

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Q: A proton traveling at 34.2° with respect to the direction of a magnetic field of strength 2.27 mT…

A: Given  θ=34.2° B=2.27mT F=9.44×10-17 N

Q: Use Green's Theorem to calculate the work done by the force F on a particle that is moving…

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Q: Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary Integer…

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Q: Use sigma notation to write the sum. 4 4 1 + 2 1 + 3 4 1 + 1 + + + ... + 4 1 + 19

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Q: Evaluate the integral. (Use C for the constant of integration.) tan (x) cos(x) dx

A: ∫tan8xcos9xdx

Q: Use a double integral to find the volume of the indicated solid. 16 15 8 TOHNWASSL 00SOTNWAS 14 13…

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Q: "JS" f(x, y) dA by dividing the rectangle R with vertices (0, 0), (4, 0), (4,2), and (0, 2) into…

A: We need to find integral.

Q: Find the curl of the vector field at the given point. F(x, y, z) = x²zi - 2xzj+yzk; (9,-9, 9) curl F…

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Q: 7. Determine the intersection, if any, of the planes with equations x +y-z + 12 =0 and 2x + 4y - 3z…

A: Since you have posted multiple questions. As per guidelines we"ll solve only first first question.…

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: Find curl(F x G) = V x (F x G). F(x, y, z)= i + 7xj + 6yk G(x, y, z) = xi - yj + zk

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Q: Find a set of parametric equations of the line with the given characteristics. (Enter your answers…

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Q: Sketch the region R whose area is given by the iterated integral. L1²5-1² dx dy

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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: Find the exact value of each expression:\\ (a) sin¯¹ (√3/2) \\ (b) cos¯¹(−1) \\ (a) \\ (b)

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Q: Find the conservative vector field for the potential function by finding its gradient. f(x, y, z) =…

A: We have to find the conservative vector field.

Q: Find the inverse function (if it exists) of f(x) = ln (1-2x). If the function is not invertible,…

A: NOTE: Refresh your page if you can't see any equations. . to find an inverse function, interchange…

Q: Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary Integer…

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Q: The indicated function y(x) is a solution of the given differential equation. Use reduction of order…

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Q: 1. Find and classify all critical points of the function f(x, y) = x² + y²-3x - 4y.

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Q: What is (cos x + x) dx? O-½ sin²x + x²/2 + C ○ -sin x + x²/2 + C O sin x + x²/2 + C O. ½ sin²x +…

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Q: Consider the following function. f(x) = 4x² - 7x² Determine whether the function is even, odd, or…

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

A: We have to find the general solution of given DE by given family of function.

Q: 2. (x+y) dx + (3x + 3y − 4) dy = 0

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Q: Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary Integer…

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Q: Identify any extrema of the function by recognizing its given form or its form after completing the…

A: The given function is fx,y=x2+y2+6x-18y+3

Q: 6. Evaluate the following real integrals by residue theorem 3 T 211 I- -S do coso + 2 sing +3 ans o…

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Q: Find the domain of the function. (Enter your answer using interval notation.) F(x)=√x + √7-x

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Q: Find the area bounded by the curve y=x^2 and the x-axis and the lines x=1 and x=3.

A: Given: y=x2, x=1, x=3, and x-axis or y=0. So, from the given curves the bounded region is as shown…

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

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