the Find the volume of the solid generated by verdoring following region about the y-axis. The region in the first quadrant bounded above the parabola y = 2x² below by the x-axis, and on the right. the line by x=1.

Q: Let r(t) = (−5t5 + 1, −4e¯5t, sin(−2t)). 1 f F (1) Find [F(t r(t)dt (don't include the +C) r(t)dt =…

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Q: Find the velocity, acceleration, and speed of a particle with the given position function. r(t)= 1)…

A: Solution is following in explanation step.

Q: Evaluate the following limits at infinity. 2³-42² 2x³+1 a) lim 100 b) lim 8118 3-41² 2z³+1

A: We need to evaluate the following limits:We can evaluate this as follows:

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A: The figure

Q: 1. Using the 3-step rule, find ƒ' (t) given f (t)= 2t+1 t+3

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Q: Let a and b be unknown constants, and de a cos bsin f(x) = a I. Determine the value of a and b that…

A: at x = -,   f(x) = acos(-)  ------- (1)  and also f(x) = bsin(-)  ------(2)from equation (1) &…

Q: differentiate f(x) = O O O O - 1 1 9x2+ 13x-5 18x + 13 (9x²+ 13x - 5) 3/2 1 (9x² + 13x - 5) 3/2 18x…

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Q: The graph of f(x) is shown below. Estimate and list the value of x where f(x) has a horizontal…

A: A horizontal tangent to a curve of a function f(x) at peaks of the function.

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Q: If the population of an ant colony in  5  days is known to be  1100  and  P'(0)=3 , what is the…

A: For Linear Growth we have formula,

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Q: Given the figure below... 18 what is the value of V. W? -18 6√5 -6√5 12 -12 6 -6 13 A 3√5 -3√5 √5 3…

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Q: 6) 3x² = 7x + 20 -3x²-3x²

A: given information

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Q: Analyze the function below. Which of the following is/are true? 8 f (d) 818 88 x+5 as x→ 1+, f (x)…

A: The function is

Q: 16. y' = (1 − y) cos x, y(t) = 2

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Q: X₁+1 = x; +h Y₁+1=Y₁+ f(x, y₁) h

A: The given ordinary differential equation(ODE) is:The aim of the problem is to solve the given ODE…

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A: given

Q: Find the local linear approximation of the function f(x) = √4+xatxo = 0, and use it to approximate…

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Q: Find the solution of the differential equation (9 - 4xy²). dy dx = = y³ such that x = 1 when y = 5…

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Q: How. 2 Evaluate the following cartesian integrals changing them into equivalent Polar integrals:…

A: The given integral is:The aim of the problem is to evaluate the given cartesian integral by changing…

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Q: 1. Use the integrating factor method to solve the following ODES. (a) (b) (c) SE SE SES dy dt dy 2…

A: As per the company's guidelines, we are supposed to solve the first three sub-parts for you, Kindly…

Q: Find 7¹(t), given r(t) = = r' (t) = (-5 ln(5t), 5√√3t, -5e-5t).

A: Given vector is as follows

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A: Given data :f(x) = Intervals given x = 4 and x = 8To find an area for two and four rectangles.

Q: Kal K² = 1¹ + 2 + 3² + +ny n (n+1) (²n+1) ( 3n² + 3n-1) 30

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Q: 3. Find the bounded area between the curves. Draw the region. y=√1-4x² [y ≤√1+x² y-4x²-1

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Q: K Find the point(s) on the graph of y = 2 x +5x-1 X where the slope is 3.

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Q: A right circular cone is generated by revolving the region bounded by y = 3x/4, y = 3, and x = 0…

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Q: Use the graph of f and g. p(x) = f(x)g(x) q(x) = f(x) g(x) y 10 8 6 4 2 f 09 g

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Q: Convert the point (x, y, z) = (-1, 5, -3) to spherical coordinates. Give answers as positive values,…

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Q: Solve the initial value problem: y(t) ty' + y = (20t² + 6t+2)y¹, y(1) = 1 (t>0) Your answer should…

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Q: X a) y = x²-1 x-1

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Q: Question A random variable X has probability density function for 1 ≤ x ≤ 4 otherwise. f(x) = { 3/7…

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Q: -10 -3 -3 -4 Ay 10- 8- 2 то 4 -6- СЫ X $10

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Q: Find f', given f(x) = x sin5 (x4) √x+1

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Q: The graph of f is shown. State the signs of f! and f" on the interval (0, 2). f'--?--0 f✔ --?-- V II…

A: From the graph, we state the signs of f' and f'' on the interval (0,2).

Q: 2³ +22²-42-5 2³-1 Consider the function f(z) = (a) Which of the following are horizontal asymptotes…

A: given function To Find: Horizontal and vertical asymptotes

Q: 2. Find y' and y" for both of the following functions. a) y = ex sin x b) y = tan x

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Q: Let y =(f(u) + 3x)² and u = x³ – 2x.

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Q: Two friends Korin and Lorie are running a marathon along a straight road. Assume that their…

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Q: Scittan tản x)(sinx) dx

A: The given integral is; 1/[(1+tan2x) (sinx-1) ].

Q: 6. Is the function given by f(x) (x + 4, for x < 3 2x - 1, for x ≥ 3 Continuous at x = 3? Why or why…

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Q: How did we get 40 in the last solution? How did we get (k+2) and (2k+1)

A: Given that :- To Prove :- Using Mathematical induction showing the left and right are equal.

Q: 8. u = i- j + k, v=i+j+ 2k

A:

Q: Find the work required to pump all the water out of a cylinder that has a circular base of radius 5…

A: We have to find the work required to pump all the water out of a cylinder.

Q: List the interval(s) on which f is increasing. The interval(s) on which f is increasing is/are (Type…

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Q: Write the equation of the vertical line at which the graph is discontinuous. Then, write what y…

A: Given

Q: Assume log x=0.31, log by=0.57, and log z=0.85. Evaluate. √xy log b z

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Q: Find 7' (t), given r(t) = (sin(t – 1), te-t, 5t ln(5t)). r¹(t) =

A: