Solve for the value of C in the equation: (3xy² + 2y)dx + (2x²y + x)dy = 0 when y(1) = 2 OA. 4 OB. 12 C. 6 OD. 8 O E. None from the Choices

Q: The degree of homogeneity of the function f(x, y) = (x² − 4y²)-¹/² O A. 1 OB.-1 O C. -1/2 D. None of…

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Q: 1. Find the domain of the following functions. Decide if the graph of y = f(x) is even or odd. (a)…

A: Domain: The set of all those values of x such that function f(x) exists at those points.A function…

Q: Use the Binomial Theorem to expand and then simplify the result: (x2 + x + 1)3.

A: Given expression: x2+x+13

Q: Question 1. Find the solution of the following differential equations (i) cos²x sin x + (cos³x)y = 1

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Q: What is the order of the equation y" y- (y')³=4?

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Q: X lim x0√1 + 8x - 1 ||

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Q: what is rational function ?

A: Relational number Our connection is number three. As you'll see that number is specific to our…

Q: Use the Binomial Theorem to expand the binomial (y - 3)4 and express the result in simplified form.

A: Given Data: Binomial: y-34

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: dy What is the IF for solving the linear equation: x + = C0SX,x >0 dx 2 O O O O A. B. D. E. MIN 3x 2…

A: To find IF

Q: Question 27 The integrating factor (IF) of the equation: (2x³y² + 4x²y + 2xy² + xy² + 2y)dx + (2y³ +…

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Q: Exercise 37. 39. A Revenue Function The revenue from producing (and selling) x units of a product is…

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Q: Evaluate the piecewise function at the given values of the independent variable. (a) f(-2) (b) f(0)…

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Q: ion-Solution-Final Answer-Conclusion forma erate solution of the first-order differential ec ent…

A: Topic:- application of integration and solution of differential equations

Q: Check if g is continuous at t=0 and t=1. If discontinuous, identify the discontinuity as remova

A: We find left hand limit and right hand limit of g at t=0 &t= 1 respectively. Then check the type…

Q: Find the volume of the solid bounded by the planes x = 0, y = 0, z = 0 and the plane 3x +2y + z = 6.

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Q: Determine the degree, order, and whether it is linear or non-linear 3 (y") ³-4y²= 10e 5x First Order…

A: Topic- Differential equations We are given an equation, (y'')3-4y2=10e5xOrder=Order of the…

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

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Q: Find f'(x) and simplify. f(x) = 8x*(x³ -9) 3 Which of the following shows the correct application of…

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Q: Question 9 Which of the following equations has a solution of the form F(x,y) = C A. 2x + 3y + (2y +…

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Q: Consider the following curve. y = √√√2+x²³ Find y'(x). y'(x) = Find an equation of the tangent line…

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

A: It is linear differential equation.so we find integrating factor

Q: tan²(x² − 1) x1 x² - 2x + 1 Evaluate: lim

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Q: 21-24 Find an equation of the tangent line to the curve at the given point. 21. y = sin x + cos x,…

A: I have appended the formula used in the solution part of the question

Q: tan² (x² − 1) - Evaluate: lim x⇒1 x² − 2x + 1

A: We have to evaluate the limit: limx→1tan2x2-1x2-2x+1

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: Evaluate:

A: Given data:- (a); 62 (b); 30 (c); 93 (d); 44

Q: t is the object's velocity when t=6? far has the object traveled in 6 hours? n is the object…

A: Topic:- application of derivatives and algebra

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: Obtain the differential equation whose general solution is y = C₁ + c₂e³x. A. B. E. y" - 3y' = 0…

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Q: Perform the indicated matrix operation, if possible. - 2x+2y -5x + y - 10x + 8y 4x-3y 4x-7y 2x 3y-3x…

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Q: Frequency A 1 5 Class width= 9 Based on the histogram above, what is the class width? 13 17 21 25…

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Q: Given the vectors a = (2,-1,3), b = PQ where P(1, 1, 1) and Q (5, 1, -1) and Ĉ = 1 + 1 + 3k. Find a)…

A: Given vectors are as  a→=2i-j+3kb→=(5-1)i+(1-1)j+(-1-1)k     = 4i-2k c→=i+j+3k    c) Projection of…

Q: which is what in decimal form?

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Q: 1 If (-x) = -5 ON) - M O O A. e5 B. ن D. E. y5 y -5 then what is the integrating factor? None of the…

A: Given: ∂M∂y-∂N∂x1M=-5y To find: Integrating factor.

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

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Q: Find the term indicated in the expansion (2x + y)6; third term.

A: Given: The given expression is: (2x + y)6 Formula Used: Binomial expansion: a+bn = C0nanb0 +…

Q: Which of the equations below is a second order nonlinear differential equation? A. B. D. E. 2 x²y-…

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Q: Find the followings a) differentiate y=(2r+5)20 (r 2+5r+3)15

A: To differentiate the given function.

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: Obtain the differential equation whose general solution is y = C₁ + c₂e³x₁

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Q: Use the Binomial Theorem to expand the expression (x3 + x-2)4 and write the result in simplified…

A: Given data:- The given expression is, x3+x-24

Q: -6 1 1 9 d. f(-4)= = -2 T Consider the graph of y = f(x) above. State the value of each of the…

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

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Q: How many x-intercepts can a function defined on an intervalhave if it is increasing on that…

A: x-intercepts of a function on a graph are the points where y has value zero i.e., when the curve…

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

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Q: 11. Let g(x) = x² e. Find at which x value(s) does g(x) have a horizontal tangent line? X

A: Given query is to find the value of x where tangent line is horizontal.

Q: If f(x) f'(x) = f'(1) = 2 sin x 3 + cos x 2(1+3 cos(x)) (3 + cos(x))² then

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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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