Conclude that the sequence (an) is a decreasing sequence, where 1 2 1 an = 1+ +.... + - In n. n Draw and annotate a picture describing what area an represents.

Q: Revenue The revenue (in dollars) from the sale of x infant car seats is given by R(x) = 67x –…

A: The objective of this question is to find the derivative of the revenue function R(x) = 67x – 0.02x²…

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Q: (d) the line x = 9

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Q: 1 5 Given f(x) = x + 1, a = 0,b = 4; n = 3; 4x₁ = 1, 4x₂ = 1,4x3 = 2; x† = 1₁x₁ = 7,x² = 3, find the…

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A: Given that,(b) using implicit differentiation to find at the point

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Q: Cost, revenue, and profit are in dollars and x is the number of units. Suppose that the total…

A: Given that the revenue and total cost functions are (a) The profit function is

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A: Here the given table shows speedometer readings at 10 second intervals during a 1 minute period

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A: Given that a solid whose base is a triangle with vertices  and whose cross sections perpendicular to…

Q: Please explain each step and graph the following: Graph the equation y= -4x2

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Q: Consider the function f(x, y) = X (defined whenever y = 0). Y (a) Find the equations of the level…

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Q: Suppose that the weekly sales volume y (in thousands of units sold) depends on the price per unit…

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Q: Problem 2: Let ?=⟨3,4,5⟩. Find a unit vector in the same direction as ?. ⟨ , , ⟩

A: u=

Q: Find the derivative of the following: Please explain in detail 2. y = x³x

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Q: 4. Find the scalar and vector projections of b onto a (a) a =, b = (b) a =, 6=

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Q: Solve for the RMS value of the sine waves below, the answer should be expressed as V0 or I0…

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Q: A swimming pool is built in the shape of a rectangular parallelepiped 12 ft deep, 10 ft wide and 15…

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Q: 7. Assume that f(x) is the original function. Describe how each of the following tran- forms f(x).…

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Q: Which of the following is true in explaining the convergence of fixed-point iteration g (x) = x + 2?…

A: Given that, the function is   ,we need to find the convergence condition of fixed point iteration…

Q: m Determine for which values of m the function (x)=x™ is a solution to the given equation. 16/0 (a)…

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Q: What is the average rate of change of the function y = 2x²+3 between x= x₁ and x = x₂?

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Q: Using the definition of continuity, show that the following function is continuous q(2) = ² at zo €…

A: The function is given byTo Show: The function is continuous at .

Q: 5. Give a direct - proof that the function f : R → R, ƒ(x) = x¹ is differentiable at 1.

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Q: Find the equation of the line in parametric form intersecting the following two planes Q: x + 2y-z…

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Q: If r(t) 0, show that r(t) = r(t) · r'(t). ‡

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Q: (sec² (sec²(t) i + t(t² + 1)³ j + t7 In(t) k) dt

A: Vector integration

Q: 2. If xy-1= 2y a) Write this equation using function notation. b) Graph the function and tell me why…

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Q: Let r(x) = p(x)/q(x), where p & q are polynomials of degree n & m, respectively. We can express p…

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Q: -5 -4 -3 -7 -2 -3 12 4 5 Use interval notation to indicate where the functin above has... A)…

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Q: Assignment 4 Problem 6: Find a vector orthogonal to both ⟨2,2,0⟩ and to ⟨0,2,3⟩ of the form…

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Q: A small radio transmitter broadcasts in a 62 mile radius. If you drive along a straight line from a…

A: Given:A small radio transmitter broadcasts in a 62 mile radius.driver drives the car along a…

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Q: For f(x)=x4, the instantaneous rate of change is known to be 108 at x = 3. Find the equation of the…

A: For f(x) =x4 the instantaneous rate of change is known to be 108 at x= 3.

Q: Find for the following dx 1- cos² (x. y)= 2y³.x²-√√x+√√2

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

Q: Evaluate the integral: (A) Let 36x² - 49 T³ dx 7 sec (0)as your trig substitution. (B) which…

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Q: The truncated conical container shown below is full of a beverage that weighs 0.5 oz/in³. The…

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Q: 26 13. Find the limits: a. lim 1+ x-+∞ 3 X X Axess M18 ANO

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Q: Let R be the region bounded by y=x², x= 1, and y=0. Use the shell method to find the volume of the…

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Q: find parametric equations for an object that moves along the ellipse (x^(2))/(4)+(y^(2))/(9)=1 that…

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Q: For y= f(x), the [Select] if this limit exists. lim h→0 f(a+h)-f(a) h > at x = a is

A: The instantaneous rate of change of f(x) at x=a is given by

Q: f(x) = 3x² - 2x-2, [-1,2]

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Q: a).y³ - 5y= 5x² + 7 point: (1,3)

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Q: Find the centroid (, ) of the triangle with vertices at (0, 0), (2, 0), and (0, 1). a=

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Q: 5. If the second derivative of f is given by f'(x) = 2x - cos(x), which of the following could be…

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Q: Find the arclength of y = 4x² - 2 on 0 ≤ ≤ 2

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Q: Find an equation of the plane containing (1, 2, −3),(0, 1, −2) and (1, 2, −2)

A: Hence the required answer isx−y+1=0Explanation:Step 1: Step 2: Step 3: Step 4:

Q: Give the largest interval I over which the solution is defined

A: Solution is giventhe largest interval I over which the solution is defined

Q: A force of 1 pounds is required to hold a spring stretched 0.5 feet beyond its natural length. How…

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