Determine the solution of the 1st Ordered Differential Equation: y(x² + y²)dx + x(3x² - 5y²)dy = 0

Q: Solve the following differential equation:    4y'' + 12y' + 9y = 0

A: we have to find the solution of given differential equation.

Q: G(x)= x³ +3x+2 x+2 [[x]] + 1 -1-x-21 - 4 x+3 + 1 x-r if x<-1 if -1 ≤ x 1 if xz1

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Q: Iculate zu for z=₁₁₁x = e Z X 2u cos(3v), y = e²usin(=

A: We are given  z=2x-yx+3y, x=e2ucos3v, y=e2usin3v we have to evaluate zu=∂z∂u

Q: Bounds

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Q: Find the G.S. (6x+y2) dx + (2xy-3y2) dy =o

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Q: Find the derivative of each of the following. A) f(x)= 125 5x B) g(x)=x³5x g'(x) = C) h(x) = log 5 x…

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Q: The graph of a function f is shown. 800 400 20 40 60 (a) Find the average rate of change of f on the…

A: we need to answer the questions from the graph.

Q: if x ≤ 2 Let f(x) = = if x > 2 If f(x) is a function which is continuous everywhere, then we must…

A: Given function, f(x)=4x-5if x≤2-3x+bif x&gt;2 Here function is continuous everywhere ,

Q: Sketch a quadric surface that could have the traces shown. Traces in x = k O k = ±2 k=+1 k=0 Traces…

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Q: Consider f(x)=5x-3-41/x^2 c) Find the equatino of the tangent line at x = 2 to the graph of y =…

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Q: Differentiate. f(x) = 8 e 6x f'(x) = [

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Q: (d) s

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Q: Find the absolute maximum and minimum values of each function over the indicated interval, and…

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Q: Given s(t) = 3t² + 3t, where s(t) is in feet and t is in seconds, find each of the following. a)…

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) √er (5 + 6e 6e)7/2 dr

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Q: g2(z) = g1(z − θ) is a horizontal translation to the: A. left B. right

A: The expression is given by g2z = g1z-θ To determine: The type of horizontal translation.

Q: x Find z. if z = xvey.x = rcos(t), v = rsin(t), when r = 2 and t =

A: Given; z=xyex/y, x=rcos(t), y=rsin(t)

Q: Evaluate I si sin³(x) cos³(x) dx .

A: We have to evaluate  ∫sin5x cos3x dx.

Q: Find the gradient off and then evaluate the gradient at the point P. a. f(x, y) = x/y, P = (2, 1).…

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Q: For the polynomial, one zero is given. Find all others. 4) P(x) = x3 - 7x2 + 15x - 25; 5

A: NOTE: Refresh your page if you can't see any equations. . the given root is x=5 so take the…

Q: A. Exact Differential Equations Verify that the following DEs are exact, then find the general…

A: Consider the differential equation               M(x,y) dx +N(x,y) dy =0…

Q: Suppose that functions f and g and their derivatives with respect to x have the values shown to the…

A: (a) 3f(x) Derivative of given combination  3f'(x) at x=2 3f'(2) = 3*17=37

Q: Find the partial fraction decomposition for the following rational expression. 2y³ + 19y2 + 48y +63…

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Q: 3) A university has 10 lecture halls. Each lecture hall has 15 rows of desks supo de With 5 desks in…

A: totak lecture halls=15

Q: Find (f 1)' (a) f(x)=3x³+4x²+6×+5₁ a=5 f(x) = x³ +3 sinx + 2 cosx, q=2 f(x) = 3+x² + ton (₂),…

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Q: 12-14 Simplify the express 12. tan(sin ¹x) 13. sin(tan ¹x) 14. sin(2 arccos x)

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Q: Given the equation of parabola y² + 4x - 2y - 11 = 0, find the following: A. Standard form / Vertex…

A: Solution is here

Q: A virus is spreading across an animal shelter. The percentage of animals infected after t days 100…

A: This question can be solved by the concept of functions.

Q: OV 7 The graph of a linear equation, y = f(x) is shown above. Find the interval where f(x) < 1.…

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Q: Use the tabular method and the properties of limit to find the limit lim ex-4 X→4

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Q: 3) If x³ ≤ f(x) ≤ x for x in [-1,1], find lim f(x) if it exists. x-0

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Q: 14. Find a y=r³ parametrization for the path that travels along the graph of z from (-1,0) to (1,0).

A: To find the parametrization of the path that travels along the graph of y=x3-x from (-1,0) to (1,0).

Q: Match the equation with its graph. x² + 2z² = 1 X* x.

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Q: Use the IVT (intermediate value theorem) to show that the given polynomial f(v)= 2v2 + 3 - 3v has a…

A: Here we have to use the intermediate value theorem.

Q: Use the substitution x indefinite integral 97dx x²√x² + 16 4 tan (0) to evaluate the

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Q: e the integral: [₂³ 1 A r² dr

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Q: Write a in the form a=a+T+aNN at the given value of t without finding T and N. r(t) @ = (?)i + (x +…

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Q: Use a grapher to find all local maxima and minima and the values of x where they occur. Give values…

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Q: lim x118 x³ + 8x 2x³ + 5x² - 2x - 2

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Q: Determine the Laplace transform of the function f(t) = t^2.  ( t squared

A: We have to find the Laplace transform of t2.

Q: A telephone line hangs between two poles 14 m apart in the shape of the catenary y = 21 cosh 5 11 -…

A: I have to answer two parts in this question.

Q: Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is…

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Q: Determine whether the improper integral converges and, if so, evaluate it.   ∞ 0 5x dx (3 + x2)2

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Q: EXAMPLES Find an equation of the tangent line to the parabola y--&x+9 at the point (2.-3). SOLUTION…

A: Find equation of tangent line

Q: 4. Determine the domain ONLY of f(x) = 4-x x²_9

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Q: Determine the missing coordinates of the points on the graph of the function. (x, y) = (-1 (x, y) =…

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Q: The loudness, L, in decibels(dB), is given by the formula L = 10. log loud in decibels is this sound…

A: Topic- functions We are given,Loudnes L, in decibels(dB) by the formula L=10·logII0where I is the…

Q: 21. f(t) = 4t 10

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Q: 1. Determine the domain and range of f(x) = 5

A: The domain of the polynomial function, fx=a0+a1x+a2x2+....+anxn is always a real number. Where n∈N…

Q: Find the difference quotient (z+h)-f(z) for the function given below. f(x) 1²+1+2 Give a simplified…

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