Find the horizontal asymptotes f(x) = = Justify your answer. 5x3 √9x6 + 4x² − 1

Q: Problem Solving 1. For the following problems, determine the area of the region between the two…

A: Solved below.

Q: Consider the initial value problem x' = 4x², x(0) = x0. For what value(s) of xo will the solution…

A: Given

Q: which means that and thus 2x 5x + 3 and g(x)= and g'(x) = D II 5x + 3

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Q: Q2A. Find the volume generated by revolving the shaded area shown in the fig below about X-axis TO…

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Q: The point x = 0 is a regular singular point of the differential equation x²y" − x(x+3)y' + (x+3)y=0.…

A: The given differential equation is x2y''-x(x+3)y'+(x+3)y=0…

Q: 1000 I(t) = 1 +999e-.6t where t is in days and I represent the number of infected individuals. 1(t)…

A: It=10001+999e-0.6t…

Q: Evaluate each indefinite i 2. (9x8+ 3x² - 4x) dx

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Q: Q) Test the convergence and divergence of the following series using ratio or root test 3n ∞ 1) Σ =o…

A: Since you have posted multiple question which is not interlinked i can do first question as per our…

Q: How do you answer question 1. Please write out each step and explain in detail what you are doing.

A: We have to find equation of Circle.

Q: Solve by homogeneous equations method (x² - 4xy - 2y²) dx + (y² + 4xy - 2x²) dy = 0

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Q: Find the area of the curve: r² = 16 cos 20

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Q: Set up the the integral to find surface area for f(x)=x^4+1 over [1,3] show all steps for setting up…

A: The solution is given below

Q: 4) The student population at a certain school here in Dagupan can be modeled by the logistic growth…

A: You must have idea about growth model to understand it better.

Q: Which of the following equations describes the partial fraction decomposition of a rational function…

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Q: Which of the following differential equations are separable? Select all that apply. 0 U 0 dy (y - 1)…

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Q: Sy² sin(3y³ + 4) dy

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Q: 9. 10. If f(x)=√ex, the derivative is: √ex a) f'(x) = Vex b) f'(x) = √ex c) f'(x) = 2x Which of the…

A: Calculate the derivative of both problem in the following way:

Q: So S/2 √xydx dy

A: solution:-∫01∫y2yxydxdy=∫01y∫y2yxdxdy=∫01yx3/23/2y2ydy=∫01yy3/23/2-y23/23/2dy=23∫01y2-y7/2dy

Q: Express the polynomial f(x)=3-12x + 21x² 16x³ + 5x4 4 f(x) = Σbi(r - 1). i=0 in the form

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Q: 21 Зл 18. If sin = and ≤0<- then tane is equal to: and s 29 2 2 21 A. tan 8 = = 21 20 B. tan 0 = --…

A: Given, sin(∅)=2129 , π2&lt;∅&lt;3π2

Q: What is the rectangular equivalence to the parametric equations? z (0) = 4 cos 0+2, y (0)=2 sin 0-5,…

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Q: What function will you differentiate to get each function? 1. f(x) = 4x³ - 6x² - 10x + 1

A: Given function is:

Q: How is vector calculated? What techniques/rules are used to find vector equation?

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Q: 3a. Find the coordinates of the relative maximum and relative minimum of the following equation:…

A: solution:-f(x)=x-32e2xf'(x)=x-32ddxe2x+e2xddxx-32…

Q: Calculate the derivative of the function below using the quotient rule. 2x ม 5x + 3 f(x) = and g(x)=…

A: Quotient Rule : If  y = f(x)g(x)  then  y' = g(x)·f'(x)-f(x)·g'(x)g(x)2.

Q: Mark heard that he could triple his money in 13 years if he invested it in a large business. What…

A: This question is related to compound interest, we will solve it using given information.

Q: Solve CO (z-2)² 3ln 2-2-¹³ +C In | x − 2 − ₂ + C None of the Above 2 ln | x − 2 + + C

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Q: What function will you differentiate to get each function? 1. f(x) = 4x³ - 6x² - 10x + 1

A: Given function, f(x)=4x3-6x2-10x+1

Q: For the next two exercises, use the Ratio Test to determine if each series converges or diverges.…

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Q: 2) If a + b + c = 0, show that a × b = b × c = cxā

A: Solve the following

Q: The length of one side of a rectangle is always three times the length of the other side. At what…

A: This is a problem related to rate of changes. Based on the general formula and concept we will…

Q: (2x² - x - 1) x³ - x² ; 2 dx

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Q: Given that f(-5)=2, f'(-5) = -4, g(-5) = -7, g(-5) = 6,

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Q: 19. Consider the integral f√x²+25 dx. 9x² a. In/√x² + 25 +x/- - b. x+ In/√x² + 25/+ √x²+25 9x √x²+25…

A: Solve the integral  √(x2+25)/9x2

Q: y' || = X y+x²y y(0) = −2

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Q: 1. what is the basic concept of a vector?

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Q: PMT is Maximum Monthly Payment = 3,504 i = 3 n = 30

A: By using given formula

Q: What is the area bounded by: 2 x² = -9y and y + 1 = 0

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Q: 14. Find the area of the curve p2 r² = 16 cos 20

A: Find the area of the given curve

Q: Problem 8. Find critical numbers of (1) f(x)=2³-3x²+1, (2) f(x)=³/5(4-x).

A: Given :f(x)=x3-3x2+1f(x)=x35(4-x)

Q: Sketch the region enclosed by the given curves. y=√x-4, x-y=4 CHOICE A y 2 3 CHOICE D 1 1 2 -21 Find…

A: The area between the curves y=x-4 and x-y=4

Q: Find fog and go f. f(x)=√√x-6, g(x) = x³ + 1 (a) fog (b) gof Find the domain of each function and…

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Q: y = √√x(x² + x³) Calculate the derivative using the product rule. f(x) = and g(x) = which means that…

A: Topic:- application of derivatives

Q: Determine the absolute extrema of the given function on the specified interval. 1. f'(x) = 3x² + 4x…

A: Given :  F'(x) = 3x^2+4x-11 = g(x)

Q: 1. Write the equation with the smallest possible shift for: a) a positive sine function b) a…

A: Let's find sine and cosine  equation from the given  graph.

Q: the convergence and divergence of the following S vergent series. b) Σ=13*51-n

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Q: Use indirect proof to show that if n is an integer and n^3 + 5 is odd, then n is even.

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Q: 3) The initial population of a certain type of animal is 5, 000. After one year, the population has…

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

Q: Q1) Test the convergence and divergence n 1) {( {1}}=1 n+1 210 – Vn 2) Σ n2+n+2 n=0 8 6n² 3) Σ n³ +1…

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