9. Determine the convergence of the following series using the ratio test. If the ration test is inclusive, state so and determine convergence with another test.

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Q: Solve for the value of C in the equation: (3xy² + 2y)dx + (2x²y + x)dy = 0 when y(1) = 2 OA. 4 OB.…

A: To find the value of C

Q: 4. Consider Line L with defining equation 2 y - ²x + 1/ . = 6 A. Find two ordered pairs (x₁, y₁) and…

A: see below the answer and calculation

Q: Solve for the value of C in the equation: O A. -5 B. 5 O C.-4 O D. 4 O E. None of the Choices dx…

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Q: (c) Let y = (In x)2. Compute y' by using logarithmic differentiation.

A: The given function y=ln x2x We have to find the derivative of y using logarithm differentiation.

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A: Let distance between camera and rocket =s ft

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A: Given a  equation of general solution of a differential equation. By terminating arbitrary constant…

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Q: Solve for the value of constant C in the equation: (2x + 3)y' = y + (2x + 3)¹/² when x = -1 and y =…

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Q: What is a suitable integrating factor that can be used to solve the equation dy dx O A. O B. 3 ex…

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Q: Please have a systematic way of solution (Question-Solution-Final Answer-Conclusion format) E.…

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Q: Find the general form of f if f'(x) = 5f(x) f(x) =

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

Q: Calculate the slope of the line that passes through (-11, -6) and (1, -4). O - 1 O -16 1 O 6

A:

Q: Consider the function f(x) = 3x²-5x+2. Use it to find f(4), f(-1), and f(a + 3). f(4) = 30 O…

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Q: Tutorial Exercise Determine the set of points at which the function is continuous. G(x, y) = In(x² +…

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Q: lim 1 - cos(sin(³-1)) 73 - 1

A: As per the instruction, we will be answering the first question. The graph of y=1-cossinx3-1x3-1.

Q: Which of the following equations is NOT an exact equation? | OA. (2x sin y + y)dx + (x² cos y + x)dy…

A: Exact differential equation A first order differential equation M(x,y)dx+N(x,y)dy=0 is called an…

Q: Which of the following equations can be made into a linear differential equation? O A. (x² + xy)dy -…

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Q: Find the particular solution of each of the following. (4+sine)y'=e*(6soc² e* - ycose); y(ln x) =…

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Q: If f(x) = = f'(x) = 4x² tan x sec x Find f'(5)= " find 4x(x + 2 tan(x sec (x) (x))

A: Topic- Derivative of a function  We are given, f(x)=4x2tan xsec xand f'(x)=4x(x+2tan (x))sec x

Q: What is a suitable integrating factor that can be used to solve the equation dy dx O A. B. e3x-3x² 3…

A: Given differential is of the form M+Ndydx=0

Q: State whether the equation is ordinary or partial, linear or non-linear, and give its order and…

A: See this solution in below.

Q: Draw the unit circle and then shade in an arc of the circle's boundary with a shaded arc length of…

A: Length of arc, l = r * theta  Where, r = Radius of circle       theta = Angle subtended by arc at…

Q: Use the first derivative test to determine all local minimum and m points of the function y=x³-6x²…

A:

Q: Which of the following statement is TRUE? 8:01 AM A. An ordinary differential equation (ODE)…

A: keeping a note ?as per our company guidelines we are supposed to answer ?️only first 3 sub-parts.…

Q: Evaluate the following integral using trigonometric substitution. x² 441-x² S dx

A: ∫x2441-x2dx

Q: Solve for the value of C in the equation: (2xy4e³ + 2xy³ + y)dx + (x²yªe¥ − x²y² – 3x)dy = 0 when…

A:

Q: Let P = 1x, y2 be a point on the graph of y = x2 - 8.(a) Express the distance d from P to the point…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: x+1=y=²¹4.

A: we wil find the required equation of plane.

Q: If ƒ(x) = 8x¹¹(»), find f'(8).

A:

Q: Constructing an Open Box An open box with a square baseis required to have a volume of 10 cubic…

A: Note:- Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the…

Q: Find all the critical numbers of f(x) = 2x4-4x³+3x²+2, then determine the local minimum and maximum…

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Q: 1. Find the limit. lim X-5 lim x-5 2 √x +11 -6 x-5 2 √√x+11 -6 X-5 =

A:

Q: Obtain the differential equation whose general solution is y = ₁ + ₂³x A. B. |y" - 3y' = 0 D. E. 3y"…

A: Differentiate both side with respect to x

Q: Which of the following equations OA. (2x sin y + y)dx + (x² cos y + x)dy = 0 OB. 1 dx-dy-0 y O E.…

A:

Q: Find the directional derivative off at P in the direction of a. ƒ(x, y) = 5x²y³; P(2, 2); a = 3 i −…

A: This question can be solved using the concept of partial derivatives and vectors.

Q: Question 2 Determine the values of a for which the following system of linear equations has no…

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Q: Use the Lagrange multipliers to find the maximum and minimum values of f(x, y) = 2x + y − 2z subject…

A: Given function fx,y,z=2x+y-2z Let gx,y,z=x2+y2+z-2025

Q: 3. Elimination of Arbitrary Contants 1. y = peax cosbx + peax sin bx 2. y = C₁x + c₂ex ; a and b are…

A: Here we have to eliminate the arbitrary constants of the equation y=ϕeaxcosbx+ψeaxsinbx…

Q: (a) J x² dx 3x + 2 x + 7 (b) 6) [ √2+1 da dx

A: Since multiple questions are asked, I am answering first question

Q: FIND F'(x) F(x) = 2 tanx 1+cosx

A: To differentiate the given function.

Q: Given f(x) = 4x¹n (x) " f'(9) _ answer the following:

A:

Q: In dx.

A: We will find  the required  integral.

Q: If f (x) = x2 - 2x, find f (a + 1) and f (a + 2).

A: Given fucnction, fx=x2-2x

Q: Evaluate the following integral. S= 2 x³√x² - 1 dx =

A:

Q: Which of the equations below is a second order nonlinear differential equation? O A. B. 2 x²y - (1 -…

A:

Q: A mathematical model for the average of a group of people learning to type is given by N(1) (2 hours…

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Q: Write an equation for each line. 15. through (2, 2), y-intercept 10

A: since you have posted multiple questions i can do first question as per our company guidellines.…