4. In the differential equation (6x–3y+2)dx-(2x- y-1)dy=0, we let the substitution dx=

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A: See the answer below

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A: Find the derivative of f(x)

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A:

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A:

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A: Explained below

Q: dx Evaluate: xV x2 + 4 x² + 4 – 4 + C x2 + 4 + 4 - A) 4 x² + 4 – 2 +C x² + 4 +2 Vx² +4-2 + C Vx² + 4…

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Q: Suppose f: I R is increasing, for some interval I. Show that lim f(x) < f(xo) < lim f(x).

A: This question can be solved using the definition of increasing function.

Q: 1. In the differential equation (x+2y-1)dx+(2x+4y-3\dy=0, we let the substitution %3= 2. In the…

A: 1) Here, the differential equation is: (x+2y-1)dx+(2x+4y-3)dy=0⇒dydx=-x+2y-12(x+2y)-3

Q: If f(x) = kx, determine the value of k that makes f(x) a probability density function on 0<xs4.

A: Given,           fx=kx2To find : Determine tha value of k that makes fx a probability density…

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A:

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Q: 13– 26, where 0 <t <3.5 (in Suppose that a particle moves along a straight line with velocity v(t)…

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A: Let's find.

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A: Given query is to find the correct option option.

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Q: Find all solutions to the equation below in the interval [0,2π)[0,2π). Give all answers as exact…

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Q: Question Evaluate the following limit using L'Hospital's rule. 10 lim 5* ( 3x2 24x +45 3x - 15…

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Q: that has i +j and i – 18j as adjacent sides. NOTE: Enter the exact answers. ||d||= 19 ||d||=|17.12

A: Vector

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A:

Q: Find y. Show the step-by-step solution. Simplify your answer. 1. y = in () 2. y = log(tan x') 3. y =…

A: 1. y=ln2x4x2-12. y=logtan x33. y=ln3+cosx3-cosx

Q: Determine whether the geometric series converges or diverges. If it converges, find its sum. E7*8*+1…

A: Given: Here,         an=7n8-n+1    =7n8n-1 So,         limn→∞an+1an=limn→∞7n+18n7n8n-1…

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A: Since, the student has mentioned to solve question number 1, so we are going to solve only question…

Q: please refer to the

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Q: ACTIVITY 2: Find the derivative and simplify the result, if possible y = x2 + n² +x" y = x2 sec x y…

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Q: Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below.…

A:

Q: Solve for x

A: For solution of f(x) = 0 Drawing the graph of y = f(x) The point where the graph passes x axis

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Q: 7s+41 s +10s +34

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Q: Evaluate the definite integral. el" i+ej+t k)dt O el7 i - e- j+ 17 k O el7 1 i- (e-- – 1) j + , k…

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Q: 2. (x+2y -1)dx+(2x+4y-3)dy =0; when x = 2 and y = -1

A:

Q: What is the limit of the following sequence? {(-1)"n'e ™ },1? 00 n=D1 О а. 1 O b. oo Oc. 0 O d. -3 4…

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Q: 2. Using Lagrange multipliers, find three positive numbers whose sum is 18 and such that the sum of…

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Q: Consider the series (-1)n*(3n2+n+5)/(4n3+2) = 5/2 - 3/2 + 19/32 - 7/22

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Q: 3. Find two linearly independent Frobenius series solutions for the given DE. You can leave your…

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Q: f(x) = x√4-x2

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Q: In how many different ways can 7 potted plants be arranged in a row with 5 spaces? O 720 O 2 520 5…

A: There are total 7 potted plantsThere are 5 spaces in a rowNumber of ways  to arrange 7 potted plants…

Q: 5. Find the indefinite integral. a) S 2*-+52 dr b) S Va(zi - a² +z)dx b) S Va(a – a² +r-)da c) S…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Question Evaluate the following limit using L'Hospital's rule. 72 6x lim -4 Lx? – 5x + 4 Provide an…

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Q: Find the area of the shaded region f(x) =Dx-8x +18x“, gx)= -20x +112 3. xg-.X%3D(x)) The area is…

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A: We will use formula for derivative of u/v and given formula to solve as follows

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A: Solve the following

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Q: In the differential equation 4(3x+ y– 2)dx– (3x+ y)dy = 0, we let the substitution dw=

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Q: Calculate the integral. (Use symbolic notation and fractions where needed.) |5 – x| dx

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

Q: If C(x) = 16,000 + 600x – 1.6x2 + 0.004x3 is the cost function and p(x) = 1,800 – 7x is the demand…

A: Given query is to find the production level where profit is maximum.

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A:

Q: Written Works Evaluate the following Integrals. 1. S sin ycosy dy 2. sin3x dx 3 1 3. Jс S cos-y dy |…

A: Given: 1). I=∫sin3ycosydy  ....(1)   As we know that; The Power rule: ∫xndx=xn+1n+1+C ; n≠-1…