1. Let R be the region bounded by y=-, the x-axis, x = 1, and x = b, where b> 1. Let D be the solid formed when R is revolved about the x-axis. Find the volume of D.

Q: log₂log 1 (x − 6) < 0 2

A: Here we are asked to solve the inequality: log2log12x-6&lt;0

Q: Find the distance of the point (4, 2, -4) from the line r(t) = (1+2t, 1+ 2t, 7 - 3t).

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Q: C] Find the domains and ranges of the following relations 1) 3) F 67 2 0 -2 2 10 2) 5 0

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Q: (a) Σ(1/7)", (b) (1/7)" where k is a nonnegative integer, n=k (c) Σ07" /n!, n=0

A: We have to evaluate the value of series in this question.

Q: Differentiate. dy dx y = 2x³ - 5x² + 7x +4 ||

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Q: e average rate of change of f(x) = 6x² - 2 on the interval [5, a]. (Your answer will be an ion…

A: Given query is to find the average rate of change for the function.

Q: 25. Sa 2x²-10x +4 (x + 1)(x-3)² dx

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Q: Problem 2 a. If y(t) = x₁(1) * x₂(t) = e^(1+3)u(t+3), find z(t) = x₁(t+4)* x₂(t−5). b. If x₁(1) =…

A: In this question we have to find the values of the functions.

Q: Consider the graph of the one-to-one function shown in the figure below. 10 y 8 6 4 2 2 4 6 8 10 X

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Q: Find dy if y=t² & t = √h and h = x² dx

A: Given data: y=t2 ,t=h and h=x2

Q: YA -3 x (a) If f is increasing on an interval, then the y-values of the points on the graph [rise…

A: Given graph of function is

Q: Calculate the cross product assuming that = (-2, -8, -2) u x w = (4u − w) × w = (100)

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Q: Find a formula for the nth term of the sequence in terms of n. 3² 3³ 34 1 3 3 - 4' 6 8 " 10 " 12

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Q: (5) A unit disk centered at the origin is sliced so that the right portion has width h. De- rive a…

A: Given fx=1-x2 width of the slice is h

Q: Given the graph of f(x) = √√x as shown, graph the function 5ƒ(x) – 5. -7 -6 -5 -4 -3 -2 -1 7- 6 5+…

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Q: 43. YA 3 -1 y=2x L (3, 3) 3x

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Q: The Differential Equation y'+y=e* has a solution y=(x+C)ex C is an arbitrary constant. IF TRUE, show…

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Q: maximum

A: The fine F for violating these limits is $10 for every mile above the maximum or below the minimum.…

Q: Which of the following is the complete set of roots of the auxiliary equation fory""-3y+3y'-y = 0.

A: Given y'''-3y''+3y'-y=0

Q: A sphere is tangent to the x-y plane, the x-z plane and the y-z plane and it's center is the first…

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Q: Evaluate [si sin 3x cos 5x dx.

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Q: D] Find composite functionsf(g(x)) and g(f(x)) for given f and g 1) f(x) = 3x + 1, g(x) = 2x² 2)…

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Q: Use function composition to determine if f (x) ar (a) Yes, they are inverse functions. (b) No, they…

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Q: Find the unit normal vector for the vector-valued function r(t)=(t^2-3t)i + (4t+1)j and evaluate it…

A: Given data:- Vector-valued function, rt=t2-3ti + 4t+1j Evaluate at t=2

Q: 1. A school auditorium has 32 seats in the first row, 35 seats in the second row, 38 seats in the…

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Q: Determine the point(s) at which the given function f(x) is continuous. f(x)=√6x +30 Describe the set…

A: We have given function  fx=6x+30 Function will be continuous if  6x+30≥0 6x≥-30 x≥-306 x≥-5 Interval…

Q: Find the area of the parallelogram with vertices: P(0,0,0), Q(-4,-5,4), R(-4,-3,6), S(-8,-8,10). 0

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Q: nd  f(a), f(a + h),  and the difference quotient  f(a + h) − f(a) h,  where  h ≠ 0. f(x) = x2 + 6…

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Q: Jane works as waitress.  Today she worked an 8 hour shift, and made $92.  Last week she worked a 5…

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Q: A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri with a…

A: Concept: Average velocity and instantaneous velocity is given by the following equation:…

Q: JJD In Exercises 7-10, evaluate the given double integral over the quarter-disk Q given by x ≥ 0, y…

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Q: does the sequence an converge or diverge? Find the limit if the sequence is convergent…

A: givenan=cos(3pi2 - 6n)

Q: Give the slope and y-intercept of the given equation, then graph it. 11. f(x) = 3x − 4 400

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Q: 3. ) Suppose Australia's aggregate income (Y) has two components: aggregate consumption (C) and…

A: This is a problem related to differential equation. Please follow the procedure given below.

Q: determine if the sequence an converges or diverges.  Find the limit if the sequence converges. an…

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Q: f(x) = √8x-6, g(x) = x² - 16, (f + g)(x)

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Q: The derivative of e" is e. What is the derivative of e? There are two functions named 'sinh' and…

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Q: 316. [T] The graph of a folium of Descartes with equation 2x³ + 2y³ - 9xy = 0 is given in the…

A: This question can be solved using the concept of equation of tangent and normal to the given curve…

Q: Evaluate the piecewise defined function at the indicated values. f(x) = 3 if x ≤ 5 5x −…

A: Given function  f(x)=3if x≤55x − 6if x&gt;5To Find: function value at  f(−6)   = f(0)   =     f(5)…

Q: Use the graph to find the average rate of change. 5) Monthly Cellular Phone Charge in Dollars 80+…

A: To find average rate of change of given function through its graph.

Q: Find a nonzero vector parallel to the line of intersection of the two planes 2y 5x - 3x = -5 and 5y…

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Q: does the series  E infinity/n=1  2^n/3^n converge or diverge a)the series converges because its is…

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Q: Graph the function. (Be sure to indicate any missing points.) ( 5x − 6 -x-5 ● No Solution Help f(x)…

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Q: 11. The table of values below shows the rate of oil consumption in gallons per minute at selected…

A: Solution: Approximate the integral ∫012f(x)dx    with the left Riemann sum using the table below:…

Q: A sports franchise revenue can be modeled by the function R(t) = 317 + 10t. Their operating costs…

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Q: The fox population in a certain region has an annual growth rate of 6 percent per year. It is…

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Q: What form of the particular solution is appropriate for the differential equationy" - y'=4?

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Q: Find the equation of the line tangent to the curve f(x) = 4x² - 6x +39 at x = 1.

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Q: b) Find the domain and the range of the following function: f(x)=√x²-25

A: Please see the below picture for detailed solution.

Q: 1. Determine the derivatives of the following functions (a) y = (x² - 2)²

A: Since you have asked multiple questions in a single request we would be answering only the first…