Evaluate: [² 3 x³dx -

Q: Praw the curve r= 4 + 8 case and find the area outside the inner loop of the curve

A: Given: r=4+8cosθ

Q: Find an equation of the plane that contains the line x = −2 + 3t , y = 4 + 2t , z = 3 −t and is…

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Q: Consider the integral fa³ In(a) dæ: Applying the integration by parts technique, let In(x) Ա dv = x3…

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Q: Find 뿐 for the ry – ln(xy) = 1 0 뽈 ㅇ-볼 O 래 ㅇ-픕 following:

A: The given expression is xy-lnxy=1 we have to find dydx use the derivative formulas, ddxx=1…

Q: I. Find the solution set of the following. 2(1 + cos x) sin x 3. tan X 2 x = [0, π] 1.3

A: Solution 1.3 Given, tanx2= 2(1+cosx)sinx,  x∈[0,π]

Q: For the following graph the equations and shade the area of the region between the curves. Determine…

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Q: 5. Prove the identity: cot(A + B) cot(A − B) = cot² B tan² A tan² A cot² B - 1 3J

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Q: The graph shows the depth of water W in a reservoir over a one-year period as a function of the…

A: Concept: The average rate of change : The average rate of change function explains how quickly…

Q: X

A: Slope intercept form of line  y=mx+b Here m=slope, b= y intercept

Q: Evaluate the following indefinite integral Show work: √ (3x² - 4x + F(x) = 1x + 5)² (3x − 2) dr. B

A: To evaluate the integral

Q: Factor the polynomial and use the factored form to find the real zeros. (Enter your answers as a…

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Q: Which of the following graphs represents (x + 1)² = 8(y - 3)?

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Q: Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the…

A: PLEASE LIKE .

Q: y = In z I at x = 1: Oy=-x+1 Oy=-x-1 Oy=x-1 Oy=x+1

A: As per the company's guidelines, we are supposed to solve the first question for you, kindly repost…

Q: Which of the following polynomials has an odd degree and a positive leading coefficient? W O -10-947…

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Q: Find two positive numbers satisfying the given requirements. The product is 182 and the sum is a…

A: Topic- Quadratic equations

Q: I. Find the solution set of the following. 2. 3x² + 2x³ — 7x² - 4x + 2 = 0

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Q: 1. √ 2x log 2x dx

A: The objective of the question is evaluate the indefinite integral. Note -  As per our guidelines we…

Q: Suppose that fo f(x) dx = = 0-4 04 O 773 O 21 O 10 7 and ₂ f(x) dx = 3. Calculate f f(x) dx.

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Q: PART D: Solving problems involving rational function, equations and inequalities. 1. Suppose you…

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

Q: Which of the following is an example of an inequality? 60 + |-3| = 63 60 + 2x < 120 60 - 2(15) =…

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Q: Find the limit and determine if the function is continuous at the point being approached.

A: This question can be solved using the concept of limit and continuity.

Q: Determine the interval of convergence of n=1 (x - 5)" n²

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Q: The route that a trolley takes around a city can be represented by the functions x² + y² = 5. A…

A: To find out the location means the points where the trolley meet the train.

Q: with

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Q: 2nx 5x e e dx

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Q: 3. Find the domain of f(x) = 1- 1 X X

A: We have to find the domain of f(x)

Q: An object moves with velocity as given in the graph below (in ft/se How far did the object travel…

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Q: 2. S (4x+5) x²+4x+20 dx

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Q: By an appropriate trigonometric substitution, Choices: √ √10 sin sin 0 cos de cos √10 sin 0 1 /10…

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Q: 10 ²S₂" f Given that answer= f(x)dx 14 3' *f*f(z)dz? 10 what is

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Q: A particle is moving with a position function given by s(t) = 6t² - in metres and time in seconds.…

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Q: Find the lengths of the functions of x over the given interval. Approximate if necessary. y=e^x on…

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Q: 5. Use the divergence theorem to evaluate the surface integral ff, F. ds, where S is the sphere x² +…

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Q: Suppose that P = f(t) is the population (in millions) of the country t years after the year 2000.…

A: Given that P= f(t) is the population (in millions) of the country t years after the year 2000

Q: The graph of a function is given. Determine the average rate of change of the function between the…

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Q: -5 -5- 0 -5-

A: Topic- Inequalities

Q: This exercise uses the radioactive decay model. The burial cloth of an Egyptian mummy is estimated…

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Q: 2x log 2x dr 1 (x²+6x+5)3/2 dr

A: As we know that; The Power Rule: ∫xndx=xn+1n+1+C   1). The given integral is: I=∫2xlog2xdx Apply the…

Q: ) Find the derivative for the function f(x)=(7x+x+10) ³/2. Write your answer using positive and…

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Q: Use the Ratio Test to determine whether the series is convergent or divergent Identify an 00 Σ (1)"…

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Q: Let G(x) = sec 0 do for a in [0,]. Find G'(a).

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Q: O

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Q: 14. y' + y tan x = sec x

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Q: 5. Prove the identity: cot(A + B) cot(A - B) = cot² B - tan² A tan² A cot² B-1

A: We have to prove the identity

Q: dt 1²+8t+20

A: We can find the answer as below.

Q: Consider points P(-1, 3), Q(1, 7), and R(-4, 9). (a) Determine the unit vector in the direction of…

A: The objective is to determine unit vector in standard form and as well as component form.

Q: ₁+∞ n(3x + 2)n n³ + 4 Given the power series Prove that the series is absolutely convergent when x =…

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Q: Two fire-lookout stations are 14 miles apart, with station B directly east of station A. Both…

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Q: The slope of the tangent line to √x+y+√√xy = 2y at the point (2,2) is:

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