1. Solve the Differential Equations. (3x² - 2y²) y' = 2xy 2. (y²_xy) dx + x² dy 3.44 Test for homogeneity 3. f(x, y) 4. f(x,y) HO tanx - sec²x - cosy 2 x² + 3xy x-24

Q: To obtain the General Solution of si What will be the form by separation of variables? cosv A)…

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Q: Define R as the region that is bounded by the graph of the function f(x) = 1-2, the z-axis, a = -1,…

A: Given problem:- Define R as the region that is bounded by the graph of the function ⇒fx=1-x22the…

Q: Write the interval of continuity for the function below: tan(cos(x)) log6 (7) f(x) = for 0x< 2π

A: The given function is: f(x)=tan(cos(x))log6xπ

Q: Find the domain and range of: 1) y = 2) y =√1-x², 3) y = x² - 2

A: We can find the domain and ranges in the below steps.

Q: Find c such that the function x ≤ c { is continuous everywhere. f(x) = x² - 3 X 6x 12 x > c -

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Q: Determine whether the three points are collinear. (0,-4), (-3,-6), (2,-2) Are the three points…

A: See this solution in below with details

Q: Find high order DE 6. (D4-5D² - 36)y = 0

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Q: Which statements are true about matrix A if a ‡ 0 and a² #b²? b b a A = a [8 There is a unique…

A: Please see the below picture for detailed solution.

Q: 2. Make up a differential equation of the form dy dt that has the function y(t) = e²t = 2yt+g(y) as…

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Q: Given that f(x) and g(x) are continuous functions, and g(4) = lim (2ƒ(x) + f(x)g(x)) = − 4 x 4 ƒ(4)…

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Q: 5. The profit, P(x), of a video company, in thousands of dollars, is given by the equation P(x) =…

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Q: Evaluate lim f(x) if f (x) x-5- A B -10-4 D 0 ∞ ∞ = 1 (x - 5) 4

A: To find out the limit.

Q: xp x + 1^₂x

A: Here is the solution:

Q: limx→0 sin 2x 2x²+x

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Q: Eliminate the arbitrary constant. y=Ax 5+ Bx³ A B 7xy "- x²y + 15y = 0 D x²y '- 7xy "+15y = 0…

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Q: If plq-r)x+q (-p)x+rp-q) = 0 has equal roots, then prove that ² = 1,1 9 Pr pr

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Q: If the general solution of (2x² − 3y²) y'= 2xyisy “¹n|yº| +xª=Cy", what is the value of b? (A) -1 B)…

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Q: 2+2x-1 dx x³-x

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Q: 9. Let f(x) = 4x² - 2x, 2 √3x- x - 6, 2, Find a) f(-1) b) f(3) c) f (8) d) f(1) e) f (6) x ≤ 1 1<x<…

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Q: Q4: Solve the following integrals:- (1) S x3-2x2 dx (2) √ √² √9-x² (3) [ xả sin xdx (cos-¹4x)…

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Q: 5. For what value of k, k> 0, does (6kx-2k) dx = -k³ ? о 1 02

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Q: Given that lim f(x) = 5 and lim g(x) = 1, evaluate the following. x→-1 x→-1 Give your answer as a…

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Q: Evaluate the integral by interpreting it in terms of areas: [*(5-32) dx =

A: Lets sketch the graph of  f(x) = 5-3x and add the vertical lines x=0 and x=4  we get

Q: Q2/Solve the following equation from t=0 to 1 with step size is 0.5 using E Method. dy -= y sin³ (t)…

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Q: Find

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Q: Evaluate the integral: ³√1 + 100x² da

A: Need to find out the integration.

Q: Solve 2log (√√x) -log(6x - 1) = 0. 1 A X=- 6 B 1 X=- 5 Ⓒx=5 D x=6

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Q: (2) S dx x²√9-x²

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: / Using Doolittles method for the following matrix A = 0 6 L-2 0 5. 087 L- matrix and U- matrix. 5…

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Q: Write the interval of continuity for the function below: tan(sin(x)) log3 (7) f(x)= = for 0 < 2T

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Q: 11. Prove the identity: tan²x tan²x + 1 = sin²x

A: Simplification

Q: x³+4x²+x-6 3 sin(-x)+3x² et f be the function defined at f(x)

A: Function

Q: Sketch the region and find its area. The region bounded by y = -8 00 8 Y -00 X 36 9+x² Calculate the…

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Q: (1) lim,-0 √x+9-3 X (2) lim-0 1–c05x x sinx (3) limx-1 x²+3x-4 x-1

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Q: 3x 9. Evaluate § 2³× d dx

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Q: Show the complete solutions. Family of circles centered at the line y = 2x. Ans: y" (y-2x) + 2(y')³…

A: Given problem:- Differential equation of family of circles centerd at the line y=2x

Q: Determine the infinite limit limx→2− x^2 − 2x/ x^2 − 4x + 4

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Q: A graphing calculator is recommended! If a ball is thrown into the air with an initial velocity of…

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Q: Find all critical numbers of each function: a) f(x) = [x^1/5]  b) f(x) = 4/1+[x^2]

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Q: Find an equation for the tangent line to the curve f(x) = x³ at the point (-2, - 8). Then choose the…

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Q: Verify if the indicated equation is an explicit or implicit solution of the given DE. y = ln…

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Q: Function 2 x + 2 Discuss the continuity of the function on the closed interval. (Enter your answer…

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Q: 30. F(x) = [sin(t²)dt . Find F '(1).

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Q: 1) Find the derivative of y with reference to < Y 블+름 2y Y

A: Here is the solution:

Q: 1) When using the Newton-Raphson method to solve the equation cos(ax) = x,this is done one of the…

A: The given equation cos(ax)=x Newton-Raphson method algorithm: The method is used to find the…

Q: Find an expression for a cubic function f if f(5) = 60 and f(−1) = f(0) = f(6) = 0.

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Q: 2) Write the equation in logarithmic form 343/3 = 7 a)log,=343 b) log, 343-7 c) log 343=7 3) The a)…

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Q: Determine which is the pure time differential equation, which is the autonomous differential and…

A: Given equations:  dfdt=e-t2                 ............................(1) y'=3y+y2…

Q: 13) 16) x2/3 x + 1 x³ x² +1 dx dx

A: Given data:- 13) ∫x23x+1dx 16) ∫x3x2+1dx

Q: 7. For the limit lim (x³ - 3x + 4) = 6 illustrate Definition 2 by finding values of 8 that…

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