Consider the following system on (-1,∞0) × (–1, 0), 2y 2x 1+ Y 1+x 1. Find all the equilibrium point(s) and determine their stability.

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A: Topic  = Trigonometric ratios

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A: This question is based on application of polar coordinates integration.

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A: Given

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Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. (- 1)*+1 3k Th...

A: The given series,       ∑k=1∞(-1)k+13k

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A: Here, an=8n5+3nn5+7

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A: We have to find the volume of the solid.

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A: By using the definition of Taylor series to find the Taylor series centered at c for the given funct...

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A: We are authorized to answer one question at a time, since you have not mentioned which question you ...

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A: topic- sequence and series  

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Q: 2х — 4 f(x) = n = 4 x + 1 P4(x) = Need Help? Read It

A: We will find the mclaurian polynomial. 

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Q: B Resort Number of rooms A Total 114 134 181 285 714 a) Determine the standard divisor. (Type an int...

A: Since only part a is visible, henc answering part a. Given query is to find the the standard divisor...

Q: The derivative of the function y = x(tan-'(3x))² is: y' tan (3x) 6x + (1+9x²) tan-³(3x)] tan (3x)[6x...

A: y = x(tan-(3x))2 dy/dx = (dx/dx)(tan-(3x))2 + x(2(tan-(3x))(3))/((3x)2 +1) dy/dx = tan-(3x))2 + 6x(t...

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A: Solution is written in below steps.

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A: We have to find the continuously serving members.

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Q: (a) f(x) = 1 – 1; I =[-2,2] (b) f(x) = I = (1,5)

A: We will find if the given function is continuous. 

Q: 12. Simplify the following rational expression for the function f (x) = 5x2 f(x + h) – f(x) h

A: Given f(x)= 5x² So, f(x+h)= 5(x+h)²=5x²+10xh+5h²  

Q: 6 (a). Let f be a differentiable function with f(0) = 1, f'(0) = 2. f(x) + f(2x) + f(3x) - 3 Find li...

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Q: 2022 2. Evaluate lim,tx (1+

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Q: Integration using Algebraic Substitution x²dx 1) S Vx+2 3

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Q: Consider the following sequence: {a, } = {n – n² }= Use an+1 - an to show that the given sequence {a...

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Q: Determine whether the series converges or diverges. n + 2 Σ nvn n = 1 converges O diverges

A: Given ∑n=1∞n+2nn We need to find whether it converges or diverges If the sum of a series equals a ce...

Q: x = -1 if y=u° +5u – 4 a

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Q: (3+2 v5)(6 - 2 V5) (4 – V5) (a) Simplify giving your answer in the form a+bV5, where d integers.

A: In this question we have to solve the following question.

Q: assume that an airplane is flying toward you at a constant height, h miles, and at a speed dx/dt. W...

A: assume that an airplane is flying toward you at a constant height, h miles, and at a speed dx/dt. Wh...

Q: For the following function, a) give the coordinates of any critical points and classify each point a...

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Q: Suppose that > an is an infinite series with partial sum SN = 7 – n=1 N2 10 16 What are the values o...

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Q: 15 10 -6 -5 -4 -2 12 3 4 5 6 -5 10 -15 Determine the equation of the polynomial, f(2), of minimum de...

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Q: Activity 3.2. Find the slope of the tangent line to the graph of the function defined by y = 4 + 2x ...

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Q: Using the figure shown, find csca (3, - 4) -5/4 -5/3 5/4 5/3

A: Here we will find  cscθ,

Q: The graph of f(x) is given by (-1,4) (1, 4) (-1,–2) (5, –2) (3,-4) (4, 5) Determine if f is continuo...

A:  Graph of the function is given, we have to find the function is continuous on the given intervals.

Q: 4. Assume y(x) = eaª cosBx is one of the solutions of the DE y(3) – 3y" + 7y - 5y = 0. Then α+β= (A)...

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Q: A circular plate with radius 6 m is submerged vertically in water as shown. Express the hydrostatic ...

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Q: Find the nth Taylor polynomial for the function, centered at c. f(x) = In(x), n = 4, c= 3 %3D P4(x) ...

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Q: The Differentiation to be made must be based on the following topics. - Exponential Function Give 3...

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Q: Write out the first four terms of the Maclaurin series of f(x) if f(0) = –4, f'(0) = 13, f"(0) = 14,...

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Q: The derivative of the function y = xe(5+sec(2x)) is: y' = [1+ 2x sec(2x) tan(2x)]e(5+see(2x)) y' = [...

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Q: Using the figure shown, find cota (3, - 4) -4/3 4/3 3/4 -3/4

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Q: Atmospheric

A: We will find the height of the mountain. 

Q: 00 Suppose that anis an infinite series with partial sum SN= 7- 10 16 What are the values of anand a...

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Q: The graph below shows the percentage of the parent atoms left vs. the number of half lives that have...

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