Separation of Variables: Solve for xy dx + (y + 1) e*dy = 0 O xe – e - y - 2y² = c O xe - e -- = C 2y2 y

Q: a) lim x-3 x+1 x2 – 4x + 4 b) lim x-2 x2 +x - 6 y? – 4y – 21 c) lim y-7 3y2 – 17y – 28 t3 +t2 – 5t +...

A: NOTE-Since you have asked multiple question, we will solve the first question for you. If youwant an...

Q: Use the Laplace transform to solve the given initial-value problem. dy — у %3D 1, у(0) %3D 0 dt

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w ...

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Q: Define f(x, y) 2x2 + y? – 2xy + 6x. Find all critical points of this function, and determine, for ea...

A: The given function is: f(x,y)=2x2+y2-2xy+6x

Q: Find the local minimum and maximum values of the function below. f(x) = 3x4 – 12x3 – 168x2 + 7 - Sol...

A: First derivative Test for Local Maxima and Minima : Firstly , solve f'(x) =0 to find critical points...

Q: x(x² +y* )° (ydx – xdy)+ y dy = 0 Ans. (x +y)' = 6y° In

A: Put x/y=p and solve it. 

Q: nd the volume of the region under the surface z = ay? and above the area bounded by a = y² and + 2y ...

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Q: Use vectors to find the lengths of the diagonals of the parallelogran that has i +j and i – 2j as ad...

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Q: Approximate the sum of the series correct to within 0.00001. (-1)" (3n)! n = 1

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Q: dations. 1. sinx siny dx + cosx cosy dy = 0

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Q: Graph the system of inequalities. Rewrite each inequality into y=mx+b form 4x+ 3y>-6 I-3y<-9

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Q: 2. * x dx V4-x4 stn-1 폭+C x2 C sin-1 + C 2 1 x2 D sin 1 x sin-1+ C sin-1 + C - - 2 O A E None of the...

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Q: b Let y = x²sin(y) + yeXy, where x = s + 2t and y = st dv when s (ii) dt = o and t =1 is [d]

A: Find your answer below 

Q: Write an expression for the apparent nth term (an) of the sequence. (assume that n begins with 1.) ...

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Q: Which of the following is a solution of the differential equation xy' +y = 4x? y = 14x-1 - 2x %3D Oy...

A: We can solve this problem by applying the concept of linear differential equation.

Q: Find the indefinite integral. (Remember the constant of integration.) | (3 + x + 4e*) dx

A: I=∫ 3+x+4ex dxI=∫3 dx +∫x dx +∫ 4ex dxI=3∫dx +∫x dx +4∫ ex dxI=3x+x22+4 ex +C

Q: u = 5i + 4j + k v = i+j+4k w = i+ 8j + 9k

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Q: Test the series for convergence or divergence

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Q: y = ² + 3 in the Cartesian form y t Express the parametric f(x). curve x t+7

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Q: 5. 5 and f are vectors such that S = 15 with a direction of 73° and = 22 with a direction of Mugnitu...

A: Find your answer below 

Q: Given f(x) has the Taylor series: Σ 2 (x – 2)" 3.3n (2n)! n=0

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Q: 37. The sales of a certain merchandising company are on their bestselling item is being represented ...

A: Let's find. 

Q: Evaluate the definite integral. dx

A: As per guidelines we can solve we can solve one question at a time so if you need more answers kindl...

Q: f (x, y) ety + 4 cos Y. (1) Find the rate of change of this function at (3, 0) in the direction of i...

A: Find your answer below 

Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your a...

A: Here we have to find the given inverse Laplace transform.     L-1[(6s-12)/{(s2+s)(s2+1)}]

Q: Consider the following. (If an answer does not exist, enter DNE.) F(x) = x/9 – x (a) Find the interv...

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Q: 3. y = 12 – 3x, y= 4 – x2

A: Given query is to find the area bounded by the curves.

Q: 14) 3sin 0 = V3 sin 0 + 3cos 0 + 3sin 0 %3D

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Q: Evaluate the iterated integral. cos(e) 3r2 sin(e) dr de

A: Given query is to find the value of the integral.

Q: 1. Write an equation of a rational function that satisfies ALL of the given the given conditions des...

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Q: Which of the following statements is false for functions f(x) and g(x) and constant c? O (c - f(x)) ...

A: Given query is to find which statment is false.

Q: A stone is dropped into a still pond. Concentric circular ripples spread out, and the radius of the ...

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Q: © If g(x, y) = In then xgx - vgw in simplified form is [c].

A: The objective is to solve partial derivative problem and explain process. 

Q: 1. f(x) = (48x* + 24x + 30) 4 -6 6. f(x) = (2x* + 1) 4 %3D - &r + 17) 3 2. f(x) = (4x* + 5x – 8x + 1...

A: solution given below..

Q: Find the vector component of v = 2i – j+ 3k along b = 2i + 4j + 4k and the vector component of v ort...

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Q: Let f(x) = x and compute the Riemann sum of f over the interval [7,8], using the following number of...

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Q: Current Attempt in Progress An oil slick on a lake is surrounded by a floating circular containment ...

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Q: Solve for all vectors X so that × X = .

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Q: sing matrices тat x + 2y = 5 x +y =3

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Q: Find the area of the triangle with vertices P(1,5, –4), Q(0,0,0) and R(2, 4, 1). NOTE: Enter the exa...

A: We know that the expression for the area of the triangle △PQR is: A=12PQ→×PR→ The given vertices of ...

Q: L is a line in 2-space or 3-space that passes through the points A ano B, then the distance from a p...

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Q: Graph the function f(x) = x + 4/x Graph the secant line that passes through the points (1,5) and (8,...

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Q: Find the indefinite integral. (Remember the constant of integration.) dx xº - 8

A: Given query is to find the value of the integral.

Q: piece of wire 26 m long is cut into two pieces. One piece is bent into a square and the other is ben...

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Q: Prove the following: sin² 0 – cos² 0 = 1– 2cos² 0 %3D

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Q: n 1.3.5. ...· (2n – 1) 5nn! n=1

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Q: Determine where the function is concave upward. ​   ​f(x)x^4-2x^3+7x+5

A: Given: - The function is, f(x)=x4-2x3+7x+5 To determine: - The concave upward of the given function.

Q: Sketch the graph of a function that satisfies all of the given conditions. (a) f'(x) < 0 and f"(x) <...

A: Given problem:- To select graph  with conditions  f'(x) &lt; 0 and F"(x) &lt; 0 for all x f''(x)&gt...

Q: A data set has n items. The sum of the items is 800 and the mean is 20. (a) Find n. The standard dev...

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Q: 15. f(x) = for every x E (-4,3] x+4 16. f(x) = sin (2) in the interval x 2-2 3 17. f(x) = { 2 - x2 i...

A: As per our guide lines we are advised to solve only first question. Please kindly upload other quest...