1. Find the center on the line y = x and passing through the origin. differential equation representing all circles with 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: Obtain the differential equation whose general solution is y = C₁ + c₂e³x₁

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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: the space curve (t) = (2t, t², 2t)

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Q: f f(x) = = f'(x) = 2x² tan x " Find f'(1) 0 find sec x 2x(x + 2 tan(x)) sec(x) B x 0

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

A: To find non exact differential equation.

Q: Which of the equations below is a second order nonlinear differential equation? A. "x²y-(1-2)² = ²x…

A: (A) Here by the square of the term (1-dy/dx)² we get the term (dy/dx)² which makes this differential…

Q: If F(x) = f(6f(5f(x))), where f(0) = 0 and f'(0) = 1. Find F'(0). F'(0) = Need Help? Submit Answer…

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Q: The integrating factor (IF) of the equation y' - 2ycot2x = 1-2xcot2x - 2csc2x

A: Given, y'-2x cot(2x)=1-2x cot(2x)-2 csc2x

Q: Given the differential equation: (4xy + 3y² - x) dx + x(x + 2y)dy = 0 The solution to the…

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Q: Find the directional derivative of f(x, y) = direction of Q(2, −2). NOTE: Enter the exact answer.…

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Q: The integrating factor (IF) of the equation: (2x³y² + 4x²y + 2xy² + xy + 2y)dx + (2y³ + 2x²y + 2x)dy…

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Q: The integrating factor (IF) of the equation y' - 2ycot2x OA sin2x OB cot2x OC.Lnsin2x D.csc2x OE…

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Q: find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P.…

A: Given expression, y=x3-3x2+4 P (2,0)

Q: In this problem you will calculate the area between f(x) = x² and the x-axis over the interval [3,…

A: a) ∆x=b-an

Q: Evaluate the following integrals: 8 3 S(4 + 3√x) (2x + √x ³) "dx

A: SOLUTION-

Q: A chemical substance has a decay rate of 6.9% per day. The rate of change of an amount N of the…

A: Given :- dNdt=-0.069N

Q: Evaluate the following integral. 48x² (x-21)(x+7)² dx Find the partial fraction decomposition of the…

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Q: Solve for the IF of the equation y(x + y + 1)dx + x(x + 3y + 2)dy = 0 OA. O B. OC. ev eLny HA O D.y…

A: given    y(x+y+1)dx+x(x+3y+2)dy=0   it is of the form Mdx+Ndy=0   where M=y(x+y+1),    and…

Q: 3. Find lim f(x) and lim f(x) for the given function and value of c. Tough X-C+ X-C f(x) = (x+8)-…

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Q: What is the standard form of this linear equation in one variable: (y + 1)dx + (4x − y)dy = 0? None…

A: Given (y+1)dx+(4x-y)dy=0 Multiply both sides by 1(y+1)dy (y+1)dx(y+1)dy+(4x-y)dy(y+1)dy=0…

Q: Which of the following is a non-homogeneous function? O tan³y/x xLnx − xlny x³ − xy + y² 3 2 - (y² +…

A: function f(x, y), if it can be written  by writing x = kx, and y = ky to form a new function f(kx,…

Q: Which of the following is a non-homogeneous function? O O tan³y/x | xLnx − xlny x³ - xy + y² (y² +…

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Q: Find the derivative: f(x) = (4 sin x + 8 cos x)tan -1 X

A: To find the derivative of given function.

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

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Q: 2. Use the graph below to determine whether the statements about the function y = f(x) are true or…

A: NOTE: Refresh your page if you can't see any equations. . as we can see from the graph, the…

Q: Question 2 Determine the values of a for which the following system of linear equations has no…

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Q: 6. Use the function and the accompanying fig following questions. a. Is f defined at x = 2? O No O…

A: Given query is to read the graph and check about the behaviour of the function on x = 2.

Q: Which among the choices is the same as the differential equation dP -= P(C₁-C₂P)? dt

A: Which of the following choices is the same as the differential equation.

Q: Find the area of the region bounded by the curves y = x² 3 x - 3x and y= 3 x 1 - 3x on the interval…

A: Let's find area of region bounded by two curves.

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

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Q: 5. Show that dy ay of dx of arccosx -1 √1-x²

A: Given that dydx of arccosx=-11-x2 We have to prove this derivative.

Q: 7x - 4 3 – – 4x 4x² dx

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Q: Evaluate the following integral using trigonometric substitution. S dx (x²-36) 3/2 " X>6

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Q: A contour map for a function f is shown. Estimate the value of fy(3, 16) 25- 20 15- 10 5 60 fy(3,…

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Q: 14. A rock is thrown vertically into the air, after t seconds the height of the rock in feet is…

A: Given query is to find the the velocity of the rock.

Q: √6 + 2x² lim x→∞ 6 + 10x [ZX][][+] [94] lim x-→-8 6 + 10x || ||

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Q: Which of the following equations is NOT a variable separable differential equation? A 2xydx + (x² +…

A: See this solution in below.

Q: Eliminate the arbitrary constants of y=ce*+₂4-sin3x

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Q: Given the differential equation: 2 y' + ²y = 6x²

A: To choose the appropriate method to be used to solve the given DE. Method 5: Exact Equation Method…

Q: Find the general solution of y" =2x+ sinx + e*

A: Topic- Differential equations We are given that, y''=2x+sin x+ex We know that,…

Q: Graph the function and observe where it is discontinuous. f(x, y) = e¹/(x - y) f is discontinuous at…

A: The given function is fx,y=e1x-y The graph of the function is as follows.

Q: K A rain gutter is to be made of aluminum sheets that are 12 inches wide by turning up the edges…

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Q: dy Solve for the value of C in the equation: + ycotx dx OA. -5 B. 5 OC.-4 D. 4 E. None of the…

A: The given differential equation is dydx+ycotx=5ecosx, yπ2=1 This is a linear differential equation…

Q: If f(x, y) = 64 - 8x² - y², find fx(1, 2) and fy(1, 2) and interpret these numbers as slopes. fx(1,…

A: F(x,y)= 64 -8x^2 - y^2

Q: Solve for the value of C in the equation: (3xy2 + 2y)dx + (2x²y + x)dy: = 0 when y(1) = 2

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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: Find the derivative of the function. F'(x) F(x) = (4x + 8)³(x² - 5x + 8)4

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Q: which is what in decimal form?

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Q: If f (x) = x2 - 3x, find f (0), f (5), f (3), and f (-7).

A: Given data:- The given function is, fx=x2-3x