Use cylindrical shells to find the volume of the solid formed by rotating area bounded by the graph of 0,0 ≤ y ≤ 1 about the line y = 1 I y and x P Volume = f(y)dy where, f(y) = What is the volume?

Q: (a) Find the average velocity of the object during the first 6 seconds. X m/s -9.8 (b) Use the Mean…

A: Given query is to find average rate of change and apply mean value theorem.

Q: Use cylindrical shells to find the volume of the solid formed by rotating the region bounded by y =…

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Q: Determine whether the function given below has an inverse function. If it does, find the inverse…

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Q: Find the tangents to the graph shown below at the origin and the point (1,1). 2x -10 B 6 10- 8 p 5…

A: Let's find tangent at origin and point (1,1).

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Q: In the following exercises, evaluate the triple integral f(x, y, z)dV over the solid B. B = {(x, y,…

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Q: - 3t 3t 2e-³t). Let r(t) = (2t — 4, 5e¯ Find the line (L) tangent to r(t) at t = = 1.

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Q: Determine the local maximum and minimum values of f(x)=2x³+3x²-12x+4 using the second derivative…

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Q: Calculate the derivative using implicit differentiation: dw dz x³w+w³+wz² + 7yz = 0

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Q: Suppose that the distance an aircraft travels along a runway before takeoff is given by D=(5/2)t²,…

A: Derivate D to find the speed and then equate that with the given speed to find the time.

Q: dx Find giving your answer in terms of m. dr 1 Given that x +4 3 I 11 $ calculate the value of m.

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Q: Find all relative extrema of the function. (If an answer does not exist, enter DNE.) f(x) = x4 - 8x3…

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Q: x² + 2x lim x 1 x² - 2x + 1

A: NOTE: Refresh your page if you can't see any equations. .

Q: A sphere is to be designed with a radius of 72 in. Use differentials to estimate the maximum error…

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Q: Write the equation of the line tangent to f(x)=x5 when x = -2. Oy=80x192 O y = -80x+128 Oy - 80x192…

A: The equation of the function is given what you need to do ? 1. Find the slope at given point 2. Form…

Q: A particle moves along the x-axis so that at any time t≥ 0 its position is given by x (t) = (at)²,…

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Q: Find the derivative of the function r = sin(0³) cos(30). dr do ||

A: Here we have r=sin(θ3)cos3θ ...................................... (1)  Differentiate with respect…

Q: adym by implicit differentiation. х2 + y2 = 36 Find dy C

A: to find out the implicit differentiation for the given function.

Q: Find the curvature of the curve r(t) = (4 + 5 cost, 0, − 1 − 5 sint) at the point t = 12 -π.

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

Q: Using the definition, calculate the derivative of the function. Then find the values of the…

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Q: Find the arc length (s) of the curve r(t) = (4t + 2, −5t + 3, 2t - 5) for - 3 ≤ t ≤ 2

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Q: Find the following using the table below. 1 2 3 4 24 1 3 413 2 g(x) 3 4 2 1 g'(x) 1 4 2 3 x f(x)…

A: Find h'(1)

Q: Part 1 of 3 Enhanced Homework Find any relative extrema of the function List each extremum along…

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Q: Find the points of inflection and discuss the concavity of the function f(x) = sinx-cosx on the…

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Q: Solve for k if h(x) = 7x+k is tangent to f(x) = x^2 +3x - 8 (Problem 16) I don’t really know what…

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Q: Determine whether the following lines intersect and, if so, the point of intersection. If they…

A: The lines first be written in parametric form.

Q: -1 [cos'x {√(1-x²)}] _dx log. { 1 + ( 1+ sin (2x√(1-x²)) (2)} TT

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Q: The height of a ball t seconds after it is thrown upward from a height of 4 feet and with an initial…

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Q: The length of a stalactite (in mm) has been measured at the beginning of every fourth year since the…

A: The solution is given below

Q: In2-1 , y=0, x= 1, and x = e. 3. Find the area of the region bounded by y= 5x"

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Q: Let f(x, y, z) = xy² + z and x = s²t³, y = st, and z = s³t³. (a) Calculate the primary derivatives…

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Q: Separation of Variables Obtain the general solution of the equation xydx - (x + 2)dy = 0

A: We have  to solve

Q: f the function rvature at x = 2. If the radius is infinite, enter 'oo' for ∞. rvature at x = 2. If…

A: We have to find the following conditions according to the given information

Q: ear approximation to the function f(x) = cos(6x) at a = π/2 is Br where and where Ris

A: Topic:- calculus

Q: For the function given below, find its inverse from the 'procedural perspective' and graph the…

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Q: Consider the following. f(x) = x(x² - 8x + 20) g(x) x² Exercise (a) Use a graphing utility to graph…

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Q: Find all critical numbers of the function ƒ(x) = sin²6x + cos6x¸ 0 < x < / Select one: a. b. C. O d.…

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Q: Calculus A kite 65 feet above the ground moves horizontally at a speed of 8 ft/s. At what rate is…

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Q: Suppose that the dollar cost of producing x appliances is c(x) = 700+ 110x-0.4x² a. Find the average…

A: We need to find cost.

Q: 6. Evaluate: secº (1/x) tan³ (1/x) dx x² | se

A: This question can be solved using integration by substitution.

Q: Match each trigonometric function with one of the graphs. 1 f(x) = tan z f(1) = CSC I f(x) = cot z…

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Q: 203. 1를 2-xdx 2 x² + x xx

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

Q: Divide using long division. State the quotient, q(x), and the remainder, r(x). 6x³-4x²+x+7 6x²+2x+4…

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Q: Separation of Variables Obtain the general solution of the equation x2 dx + y(x-1)dy = 0

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Q: Evaluate the following limit: lim O O O - 7Inx lim x+19x³-9 - 7Inx lim x+19x³-9 lim x+19x³-9 - 7Inx…

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Q: Suppose that the height of a particle is given by s(t) = t³ - 17t + 41, t≥ 0, where t is measured i…

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Q: A boat is pulled into a dock by means of a rope attached to a pulley on the dock. The rope is…

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Q: Consider the function f(x)=5√x+9x^3+6x f′(x)=

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Q: Determine the quadratic function f whose graph is given. The vertex is (2, -1) and the other given…

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Q: Identify the equation as a homogeneous or exact equation differential equation. then solve the…

A: Given differential equation is first order, non linear ,homogeneous differential equaton