7. Set up a definite integral by using a Riemann sum to find the volume obtained when the region between y = x¹, y = 8x is rotated about the line y = -2.

Q: d d Question 1 Use the quotient rule to derive the formula for csc r and for cot z. dr da

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Q: 1. Write a polynomial function that has these zeros: 0, -2, 6i.

A:

Q: Find f'(x) for f(x) = 8x³. f'(x) =

A: To find .

Q: Find dy dx 1) y = -1/323 ; tan 43 2 y = sec 5x 3) y = cos cos 2x + tan¹ \/ / 4) y = cot²¹ 2² 2 5) =…

A: Note:-Since you asked multiple questions, according to our policy we can answer only first question…

Q: Find the indefinite integral using an appropriate trigonometric substitution and showing a right…

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Q: A manufacturer estimates that its product can be produced at a total cost of C(x) 40,000+ 100x + x²…

A:

Q: 1. The average rate of change of f(x) = (x − 1)(x + 2) over the interval -1 ≤ x ≤ 1 is a. -2 b. 1 C.…

A: To find the average of change of  over the interval .Note: Since you have posted multiple questions,…

Q: If y = f(x), then f'(x), y', [Select] dy da and f(x) all represent the of fat x.

A: If , then to determine the meaning of .

Q: Given f(x) = -4x + 2, find the following. (a) f(-1) 6 (b) f(0) 2 (c) f(1) -38 X Awesome! You're…

A: a) f(-1)=6 b) f(0)=2 c) f(1)= -2Explanation:

Q: Find a geometric power series for the function Select one: है n=0 6" + 1 a. O b. OC. Z Ž x" n=0 6²+1…

A: The given function is . The geometric power series of the above function is required.

Q: 11. The average rate of change of f(x) = (x-a)² over the interval a ≤ x ≤a + 1 is C. 1 d. -1 a. 2a…

A: Solution is following in explanation step.

Q: Find the work done for a force F=36/x^2 N from x =1 to x=6 m.

A: The objective of this question is to calculate the work done by a force that varies with position.…

Q: For the function f(x) = 2x² - 4, evaluate the following, enter your answers in simplest form: f(a+h)…

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Q: p(x) = 85 - 3x x (Millions) 1 4 8 12 16 1≤x≤20 Revenue Revenue R(x) (Millions S) 82

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Q: 27. Determine the average rate of change of f(x) = 2x³ — 1 over the interval 1 ≤ x ≤ 3.

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Q: n+1 Σ()" n=0 (x + 2)"

A: We have to determine the interval of convergence for the power series

Q: The exponential model A = 735.9e0.01t describes the population, A, of a country in millions, t years…

A: Year is 2028Explanation:

Q: Problem #2. Calculate the exact value of the distance from the plane given by 3x-y + 2z = 6 and the…

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Q: 1 a cos x + b sin x + c a, b, c > 0, c> a, c + a c - a dx 9 where b с a 2

A:

Q: Find the domain of the vector functions, r(t), listed below. using interval notation. a) r(t) =…

A: Domain is the reach of independent variable

Q: Find the area of the cosine curve between and

A: Since you have asked multiple questions, we will solve the first question for you.If you want any…

Q: nt A=P [₁ + 1)² )" Use the compound interest formulas A = P and A = Pet to solve the problem given.…

A: a. The accumulated value if the money is compounded semi-annually is $18,173.21b. The accumulated…

Q: Integrate: 22 3 + 2x + 10 - dx

A:

Q: Estimate the derivative from the table of average rates of change. HINT [See discussion at the…

A: To estimate the value of derivative from the table of average rate of change.

Q: Given f(x) = −4x + 2, find the following, f(y)=

A: Hence,f(y)=−4y+2Explanation:Step 1:Given that f(x)=−4x+2 Step 2:To find f(y), we simply replace x…

Q: 13. Evaluate the limit for the graph: lim¸(1 − x + x²) Xx→-1 a. 0 b. 1 14. Evaluate the limit for…

A:

Q: Find the limit: <0.00) lim t-0 -9t t 48 10 " t⁹ - t8' 16+t'

A: The given limit,.The objective is to find the limit.

Q: 3) An observer on the roof of a 40 ft building measures the angle of depression from the roof to a…

A: Given that the observer is standing on the roof of a building and observes a bench on the ground, we…

Q: 8-х, х4.

A: f(x)={8−x,x&lt;43x4+2,x&gt;4

Q: Find the slope of the graph of the function at the given value. f(x)=-4x²+6x- when x=-3 802 9 a)…

A:

Q: Write an equivalent series of the series n = 4₁ Select one: O b. O a. O C. d. e. M8 M8 M8 M8 IM = 4…

A: The given series .The objective is to rewrite the series that begins at .

Q: Problem #4. Give the component form of the unit tangent vector for the function r(t) = (t cos(t), t…

A:

Q: An object moves along the y-axis (marked in feet) so that its position at time x (in seconds) is…

A: Position of An object at time x(in seconds) is given by the functionf(x)=x3−12x2+45x

Q: 7. dy dt +2y=e¹/³, y(0) = 1

A: Here a Initial value problem is given. We use Integrating factor method to solve this Initial value…

Q: The curve in the plane defined by the equation (*) (x^2 + xy + y^2 = 7) is a rotated ellipse, shown…

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Q: For the function f whose graph is given, determine the following limits. lim f(x) and lim f(x) x-1…

A:

Q: Please solve the problem step by step

A: Answer:   Complex zeros : i3​ , −i3​Explanation:Step 1:

Q: Suppose you pluck a guitar string and watch it vibrate. If we think of theguitar string as stretched…

A: Refer to explanationExplanation:a. To describe the cross sections of the function…

Q: Find parametric equations for line that is tangent to the curve x = cost, y sin t, z =t at the point…

A: Given point is,.

Q: Find the arclength of the curve r(t) = (2t2, 2√2 t, Int), for 1 ≤ t≤ 8. L=

A:

Q: Find the average rate of change of the function over the given intervals. f(x) = 5x³ +5; a) [2,4],…

A: GivenTo Find:To find the average rate of change of function over the interval

Q: nd an equation of the plane. the plane that passes through the line of intersection of the planes x…

A:

Q: Define vectors a= and b= and compute the following. Show work and explain reasoning

A: The given vectors are  and

Q: Find the value(s) of c such that the area of the region bounded by the parabolae y = x² - c² and y =…

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Q: 30. Given g(x) = 3x² + 2, use the difference quotient to find the instantaneous rate of change when…

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Q: Compute the derivative of f(x) = 5 tan(x) sec(x).

A: f(x)=5tan⁡(x)sec⁡(x)Product Ruleddx[f(x)g(x)]=f(x)g′(x)+g(x)f′(x)

Q: For the function f(x) = = f(x+h)- f(x) h 7 x " evaluate and simplify the difference quotient:

A: For the function , to evaluate and simplify the difference quotient.

Q: Starting from the point (-3, -2, -2) reparametrize the curve in terms of arclength. r (t (8)) =i+ j+…

A:

Q: Identify the interval of convergence of a power series Σ(-16)".x²n n = 1 Select one: a. O b. O C. O…

A:

Q: Ex 7. Create a table (and a graph) of values of f(x) conjecture about the value of lim f(x). x 3…

A: x 2.912.922.932.942.962.972.982.993.0f(x) =…