Given an ordinary differential equation in the form: (xy + y² + y)dx – (x + 2y)dy = 0 (Eq. Test the exactness of the differential equation. Consequently, obtain the general solution of the equation.

Q: Given the equation y = exp(ax^(1/2)+b), which of the following plots will give you a straight line i...

A: Compare the equation with straight line equation.

Q: Equation Find Given dy dx 3. y = (a) when x = 4 %3D dt dt dx dy (b) when x = 25 = 2 dt %3D dt

A: Solution: y=x 

Q: 1. (5 points) Given the equation of a circle 2x2 + 2y2-32x + 12y + 90 = 0 Rewrite it in the standard...

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Q: Find the linearization L(x) ofy = e8# ln(x) at a = 1. L(x) =

A: We will use formula for linearization at one variable.

Q: C 12 A 34 37 В

A: The given triangle has side lengths,AC=12, AB=37, BC=34

Q: 2x - 3x - 21х -2х + 24 y = 2x* – 7x' – 11x² + 22x + 24 E. Infinite discontinuities F. Removable disc...

A: Here we have to find out the infinite discontinuities and the removable discontinuities

Q: 49. x = f(p) = 950 – 2p – 0.1p - - (A) p = 30 (B) p 50 (C) p = 70 %3D %3D

A: We will use the price demand equation at find the demand is elastic . unit elastic or inelastic.Belo...

Q: The function f(x) = 6x In(1 + x) is represented as a power series f(x) = E > Cnt". n=0 Find the spec...

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Q: Evaluate f x+3 x3+27 dx.

A: Our Aim is to evaluate the integral given below:-∫x3+27x+3dx -(i)

Q: a. What is the radian measure of an angle that measures 240 degrees? Give the answer as a simplified...

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Q: M(x,y) dx + (xe*y – 4xy + 2) dy = 0

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Q: 3. (D5- D-2D3 + 2D2 +D – 1)y = 0

A: This is a differential equation problem

Q: Let s = f(t) give an object's height, in feet, a seconds after it is thrown. After 3 seconds, tE fee...

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Q: Use Newton's Method with the function f(x) = x² – 2 and initial value xo = 3 to calculate æ1, x2, X3...

A: Newton's approximation method is used .  x1,x2,x3 are calculated or n =0,1,2 respectively.  

Q: Draw a graph of the cosine function with an amplitude of 12 (show at least 2 full periods).

A: Draw the graph of the cosine function with an amplitude of 12 . 

Q: (x+6)dx 4. S (æ+2)?

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Q: Find the equation of the line tangent to the graph of f(x) = (In x)4 at x = 5. (Type your answer in ...

A: Given that: f(x)=(lnx)4

Q: (b) What is the average rate of change in the size of the tumor during the first two months? Round y...

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Q: cos z) dz 4 5.

A: Given: - The indefinite integral is, ∫e2zcos14zdz To find: - The solution of the given integral.

Q: A point on a rolling circle of radius traces out a cycloid, which can be parameterized by c(t) = (Rt...

A: We have to show  that the length of this arch is always four times the diameter of the rolling circl...

Q: How many transformations must be applied to the graph of the function f(x) to get the graph of the f...

A: The transformation from f(x) to g(x)=2f(2-x)+2

Q: Find all the values of a such that the given series would converge. (– 1)"9"x" Σ n=1 (Vn+ 5) The ser...

A: Here we have to find the values of x such that the given series would converge.

Q: Show Intro/Instructions Suppose f is a quadratic function that has roots at 3 and x = 6, and f(0) = ...

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Q: a. Suppose f(x) = 17x* + 16x² + 6x – 13. Determine the degree of f. Preview b. Suppose g(x) = 7x³ De...

A: Topic = Polynomial   To find the degree of the polynomial, add up the exponents of each term and sel...

Q: Given the differential equation y" + 4y' - 12y = 10x2 + 7 And the Solutions to its Characteristic Eq...

A: NOTE: Refresh your page if you can't see any equations. . given characteristic solutions are  for ...

Q: 8. Let f(x) = x3, g(x)= sin(x) and h(x) =Vx. Evaluate the following functions. a. h (g ("/2)) b. Dom...

A: f(x)= x3 , g(x)= sin(x) , h(x)= √x ,  Evaluate  a)h(g(π/2))  b) domain of g(f(x))  C) range of f(g(x...

Q: Find the antiderivative of 5$sinx ln 5 cos x dx. A.) 5cosx + C B.) 5sinx + C C.) 5sinx In 5 + C 5sin...

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Q: (1+2 In æ)4 6.

A: topic - indefinite integral

Q: Determine if the given function is continuous on each of the given intervals. A. f(x) = 3x³ + 4x² - ...

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Q: An object is shot upwards from ground level with an initial velocity of 3 meters per second; it is s...

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Q: 25. A 10-foot ladder is placed against a vertical wall. Suppose that the bottom of the ladder slides...

A: Given :-  dx/dt= 3feet/sec  Ladder height= 10feet  Find rate at which ladder is sliding down from th...

Q: Find the value of k so that the value of f,"(2y – 1) dy is 10. 1 2 4 A) в B) c A D) D 3.

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Q: The left side is more complicated, so start with it. Use a Pythagorean identity to simplify 4 cos? B...

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Q: Find all the values of e such that the given series would converge. (z – 11)" n( – 7)" n=1 The serie...

A: series

Q: 18( cos54 + isin54°) 3(cos102" + isin102" )

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Q: What is the position function?

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Q: In Problems 59-66, use the price-demand equation to find the values of p for which demand is elastic...

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Q: Find f, (X,y) and fy(x,y). Then, find fx(-3,1) and fy(-4, - 2). f(x,y) = - 2xy + 3y + 8

A: Given that: f(x, y)=-2xy+3y3+8

Q: Find the general solution of the differential equation æyl + 2y! – (x + 2) cos (x) + y = 0 and choos...

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Q: 29. f(x) = (x* + 1)-2 %3D

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Q: 1. S (7x³ + 4x² ) dæ

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Q: dy +7"y – 7= 0 can be classified as dx The differential equation order 1, linear, and homogeneous or...

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Q: v(v² –1)dv v² +1

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Q: Consider the following rational function: 1 anx" + an – 1x" + ajx + a0 ... f(x) bmxm + bm – 1xm + .....

A: Recall: Horizontal asymptotes of a rational function : Consider the rational function               ...

Q: Hannah buys 2 dozen roses. Of these roses, are red, and the rest are white. How many white roses doe...

A: We need to find number of white roses.

Q: If 5dx + 1 = 2, what is the value of b? 48x2 А.) 2 В.) 4 С.) 8 D.) 9 А) с B D D) A

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Q: In Problems 17-34, find f' (x) and simplify. 17 fl .. 10 T U.2x, -2X 5. J(x) = 6e¯ 26. flr 28 (4+ 3)...

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Q: If f(-2) = 2, write an ordered pair that must be on the graph of y = f(r + 4) – 3

A: Ordered pair represents the position of a point. X axis represents the left or right position , if l...

Q: 15 4 -4-3 -2 4 2- -3 3.

A: Accordimg to given graph a. As x→-2-  fx→∞b. As x→-2+  fx→-∞

Q: the rate of change in thr profit (p) with respect to the number of units sold (x) is 0.0006x^2 +10. ...

A: We can use the given equation to solve for profit