Use the washer method to find the volume of the solid obtained by rotating the region bounded by y = x² and x = y² about the line x = 1. Give the exact answer, not a decimal approximation. y ✓ (1, 1) y=x² X

Q: Which of the following equations is NOT an exact equation? OA. (2x sin y + y)dx + (x² cos y + x)dy =…

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Q: aluate the integral. [29 tan 29 tan 5x sec 4x dx

A: The given integral is  ∫29tan5xsec4xdx

Q: the space curve (t) = (2t, t², 2t)

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Q: Obtain the differential equation whose general solution is y = ₁ + ₂³x

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Q: Evaluate the following integral using trigonometric substitution. x² 441-x² S dx

A: ∫x2441-x2dx

Q: Obtain the differential equation whose general solution is y = C₁ + c₂e³x. OA. B. U O y" - 3y' = 0…

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Q: (Question-Solution-Final Answer-Conclusion format) E. Generate solution of the first-order…

A: The solution of given exact differential equation is as follow.

Q: Eliminate the arbitrary constants of y=c₁e*+cx*— sin3x

A: We use differentiation to Eliminate the arbitrary constant, we differentiate the given equation as…

Q: Geometry A wire of length x is bent into the shape of asquare.(a) Express the perimeter p of the…

A: Given: A wire of length x is bent into the shape of a square. (a) To express the perimeter p of the…

Q: 8. Find the limit of f(x) = lim f(x)= 4- 818 (Type a simplified fraction.) lim f(x) = 8118 (Type a…

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Q: Which of the following equations has a solution of the form F(x,y) = C A. 2x + 3y + (2y + 3x) dy: dx…

A: Option D :   (A) and (D) Does not have  a solution  of the form F(x,y) =C

Q: The integrating factor (IF) of the equation y' - 2ycot2x O A. sin2x O B. cot2x O C. Lnsin2x O D. E.…

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Q: The rate of change of the variable y in terms of another variable t is equal to the expression 5t4 -…

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Q: a. Graph the functions ƒ(x) = x/2 and g(x) = 1 + (4/x)together to identify the values of x for…

A: Given:-f(x)=x2g(x)=1+4x

Q: Tutorial Exercise Determine the set of points at which the function is continuous. G(x, y) = In(x² +…

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Q: State whether the equation is ordinary or partial, linear or non-linear, and give its order and…

A: See this solution in below.

Q: p(x)=3x^3−x^2−8x−25 k=3 Use synthetic division to determine if the given value for k is a zero of…

A: The given polynomial is  P(x)=3x2-x2-8x-25  check whether k=3 is a root of the polynomial or not.

Q: Evaluate the following integral. 4x Jetz 4* sin(2x) dx =

A: The given integral is e4xSin(2x).

Q: Which of the following equations can be made into a linear differential equation? O A. (x² + xy)dy -…

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Q: Given the plane л: 2x + y - 3z - 2 = 0, and the lines l₁: 2 - x = = Z-4 3 2 a) Find a set of…

A: The givne plane is π: 2x+y-3z-2=0 ........................................ (1)  and the lines l1:…

Q: Solve for the value of constant C in the equation: (2x + 3)y' = y + (2x + 3)¹/2 when x = -1 and y =…

A: To solve for the value of constant C in  the equation: 2x+3y'=y+2x+312when x=-1, and y=0.

Q: A mathematical model for the average of a group of people learning to type is given by N(1) (2 hours…

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Q: What is a suitable integrating factor that can be used to solve the equation dy x + 2y - 4xy - e-*…

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Q: f(x)=(2x+1)^4. A) Find an equation for the tangent line to the graph of ff at x=2…

A: Givenf(x)=(2x+1)4

Q: lim x→7 x-7 14 x² - 7²

A: SOLUTION-

Q: What is the standard form of this linear equation in one variable: (y + 1)dx + (4x − y)dy = 0? |…

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Q: Given the following functions: f(u)=u^5/2 and g(x)=x^6+1. Find f(g(x))= f′(u)= f′(g(x))= g′(x)=…

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Q: Find, correct to the nearest degree, the three angles of the triangle with the given vertices. A(1,…

A: First of all find side length using cosine formula and distance formula

Q: 1. Find the center on the line y = x and passing through the origin. differential equation…

A: Need to find out the differential equation that represents the circles with center on the line y=x…

Q: Find y'(x). y'(x) = y = √-1 + 2x At what point on the given curve is the tangent line perpendicular…

A: Given query is to find the derivative and the point where slope of tangent is perpendicular to the…

Q: At t = 0, a train approaching a station begins decelerating from a speed of 104 mi/hr according to…

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Q: Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.…

A: degree of polynomial=2zeros x=-2 and x=7

Q: Use a Riemann sum with 4 rectangles of equal width to approximate the area between y = x³ +8 and the…

A: Let's find area by using right hand Riemann sum.

Q: 2. Find the 2nd derivative of sin (x²-1) y *2cos(x^2-1) 4x^2 tan(x^2-1) 2cos(x^2-1) + 4x^2…

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Q: Which of the equations below is a second order nonlinear differential equation? O A. 2 ¯\x²y - (1 -…

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Q: If you roll a 1-m-diameter wheel forward 30 cm over levelground, through what angle will the wheel…

A: Given data:- The given you roll a 1-m-diameter wheel forward 30 cm over level ground. Formula used,…

Q: List the intercepts and test for symmetry: y2 = x + 4

A: Given data:- The given equation,y2 =x+4

Q: Solve for the value of C in the equation: dy − (y + xy5)dx = 0 when y(0) = 1 - A. 1/4 B. 1/2 C. 3/4…

A: Find integration factor first as it is linear differential equation

Q: Evaluate the following integrals: 2 5cos x - 3tan x COS X S- -dx

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Q: Solve for the value of constant C in the equation: (2x + 3)y' = y + (2x + 3)¹/2 when x = -1 and y =…

A: We have to find the value of c.

Q: Let ƒ(x) = x/x - 2. Find a function y = g(x) so that (ƒ ∘ g)(x) = x.

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Q: State whether the equation is ordinary or partial, linear or non-linear, and give its order and…

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Q: A certain drug is eliminated from the bloodstream with a half-life of 34 hours. Suppose that a…

A: Given half life of 34 hours Initial does of 75 mg

Q: Which of the equations below is a second order nonlinear differential equation? O A. ¹^²x²y — (1 —…

A: We have to find second order non linear differential equation from given options.

Q: If sin(0) = 3 - and is in quadrant II, then find the EXACT value of sec(0). "

A: Given that sinθ=35 Use, the formula sinθ= PH Where P is the perpendicular and H is the hypotenuse.…

Q: Use limits involving to to describe the asymptotic behavior of the function from its graph. (If an…

A: From graph f(x) goes towards 1 at left end of graph

Q: Solve for the value of C in the equation: (2xy4e³ + 2xy³ + y)dx + (x²yªe¥ − x²y² – 3x)dy = 0 when…

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Q: 7. Find (a) the slope of the c y=9x² -1; P(4,143) (a) The slope of the curve (Type an integer or a…

A: solution:-y=9x2-1slope= dydx=ddx9x2-1=18x(a)slope of tangent at point P(4, 143)slope = 18(4)=72

Q: (b) Let y = (2x + 1) cos. Compute by using logarithmi dy dx

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Q: 14. x+5 x²- x - 14x +45 Describe the set of x-values where the function is continuous, using…

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