PART III: Solve the following problems. 2. The sum of two positive numbers is 2. Find the smallest value possible for the sum of the cube of

Q: Question 5 Which values fall within the range of this function? f(x) = -4x+3+2? Select all that…

A: To determine the value that falls within the range of  the following function. fx=-4x+3+2

Q: Construct a limit evaluation problem with an answer of 1. (do not use L'Hospital's rule)

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Q: When finding the moment produced by a three-dimensional force we commonly use the equation M = r X…

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Q: Construct an equation that has an absolute maximum of 5 when graphed. Please show steps.

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Q: [b] Take a limit of the standard slope formula, as shown below, to find the instantaneous rate of…

A: The given function is gx=x2+2x. To find the derivative at x=2 and the equation of tangent line at…

Q: The radius of a right circular cone is increasing at a rate of 1.2 in/s while its height is…

A: given radius of a right circular cone is increasing at a rate of 1.2ins and height is decreasing at…

Q: Construct a problem where you have to find the inflection point that is equal to 1/2.

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Q: 3+3=? Please explain

A: To find the value of the following expression. 3+3=?

Q: Suppose f(x) = 2 + 8x². Determine, in a simplified form, each of the following: (a) f(a) = (b)…

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Q: d. f(x)= sinsin (2x) coscos (x)

A: To differentiate the following function. fx=sinsin2xcoscosx

Q: Find the rate of change of ƒ (x, y, z) = 6xyz in the direction normal to the surface yx² + xy² + yz²…

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Q: 1. Differentiate the following functions f(x)= f(x) = x² cos(x) a. b. f(x) = sin²(5x) c. f(x) = sinx…

A: The given functions, a) fx=x2cosxb) fx=sin25xc) fx=sinx cosx We have to find the derivative of each…

Q: t said to use x 4

A: To solve the questions.

Q: If a company's marginal revenue function is MR(x) = xe-x/2, find the revenue function. [Hint:…

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Q: Let f(x)=2x² - 6x² - 48x + 6. a. Find all points on the graph of f(x) at which the tangent line is…

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Q: The total number of acres of genetically modified crops grown worldwide from 1997 to 2003 was…

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Q: Cheap Chips Corp. has determined that the profit, in dollars, derived from the production and sales…

A: Given profit function  p( x ) = 2000xe-x40 Where profit in dollars  x is the units sale

Q: Solve the given differential equation by separation of variables. 1 y In(x) dx = (v + ¹)² dy x³ln(x)…

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Q: The total cost function for a product is C(x)=700ln(x+100)−100, where x is the number of items…

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Q: 14x^2-13x-12 using factor by grouping

A: let  K=14x2-13x-12

Q: Find the distance from the point S(-2,-1,6) to the line x=2t, y = 10t, and z = -1t. The distance is…

A: point s-2,-1,6line x=2t, y=10t, z=-1t

Q: f(x, y) = e cos(ly). Find and classify all critical points of the function. If there are more blanks…

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Q: Perform the indicated integration using INTEGRATION BY PARTS 1. √z. In z dz

A: To perform the indicated integration by using integration by parts. ∫z·lnz dz Note: Since the…

Q: olve question 2 please. Explain in an easy to understand way

A: Graph of f(x) is given . We have to find why the derivative of a sinusoidal function is also going…

Q: Find equations of the normal and osculating planes of the curve of intersection of the parabolic…

A: The curve of intersection of the parabolic cylinders x = y2 and z = x2 at the point (1, 1, 1). Find…

Q: Determine the slope and the equation of the tangent to the curve f(x) = sin(x) + sin(x) at x=

A: f(x)=sin2x+sinx at x=π

Q: Assignment: Consider the region bounded by the parabolas: 2 2 y = x² + 4x + 3 and y = x + 2x + 3.…

A: We need to find volume.

Q: 3) Factor the following polynomials: (a) 12x²y + 4xy² - 18ay (c) 2x² - 9x - 18 (d) 27y³ - 125 (b) d…

A: Given polynomials are : (a) 12x²y+4xy²-18xy ;  (b) d²-5d-66 (c) 2x²- 9x - 18 (d) 27y³-125 (e) 121x²…

Q: that the indicated family of functions is a solution of the given differential equation. Assume an…

A: The given differential equation is;  d2y/dx2 - 6dy/dx + 9y=0

Q: If the velocity of a moving object is t 2 1² v (t) = 20 2 in meters per second, then what is its…

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Q: Compare the functions f(x) = x³ and g(x) = ex by graphing both functions in several viewing…

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Q: The equation for the price of a television, based on the demand, is P(x)=175-0.4e0.001x What should…

A: The equation for the price of television based on demand is P(x) = 175 -0.4e0.001x. Our task is to…

Q: need help with this question: Find the equation of the tangent line to the graph of the equation…

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Q: 1. Determine the derivative with respect to 'x' of: a) f(x) = 4cos(x³) - sinx b) f(x)=x² cos² (5x)…

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Q: A bicycle wheel has radius R. Let P be a point on the spoke of a wheel at a distance d from the…

A: Given          parametric equations…

Q: A jumbo jet maintains a constant airspeed of 500 miles per hour (mi/hr) headed due north. The jet…

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Q: Consider the two functions f,g: [−1,5] → R, whose graphs are given below. 4 y = f(x) y = g(x) 3 3 2…

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Q: 2. Determine the cartesian equation for a line that passes through the point (4,-3) and is…

A: The line passes through the point 4,-3 and is perpendicular to the line r→=2,-3+t5,-7 Therefore, the…

Q: Please answer and explain

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Q: 29 / 36 determine the derivative function (for). 9. Let f be the R²R function defined by f(x, y) =…

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Q: Use the Shell Method to compute the volume of the solid obtained by rotating the region in the first…

A: Given functions are, y=x4 & y=x4 about y-axis

Q: Kelly and Stuart bought potato chips for a party at the same store. Kelly spent $14.15 for 3 large…

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Q: Perform the indicated integration using RATIONALIZING SUBSTITUTION 3 dy 4 + ³√y+1 1.f.

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: (2) Given f(x)= numbers √x+2c_if x>4 [ex² if x≤4 find the value of c so that f(x) is continuous for…

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Q: 3. Use the Intermediate Value Theorem to show that there is some c in the interval (-1,0) at which…

A: f(-1) = (-1)³ - 3(-1) + 1 = -1 + 3 + 1 = 3.  f(0) = (0)³ - 3(0) + 1 = 0 + 0 + 1 = 1.

Q: Find the area of the region enclosed by y = 3.25x and x = 7.5-y². 2 2 1 2 w A 5 6 N Use horizontal…

A: The area bounded by the curves x= f(y) , x= g(y) between y= a and y = b is given by A = ∫abfy-gy dy

Q: II. Find a vector parametrization and parametric equations for the line with the given description.…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Given the function f(x) = -2x³ +96x + 1, determine the intervals where the function is increasing…

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Q: In this problem, y=c₁ex + c₂e-x is a two-parameter family of solutions of the second-order DE y" - y…

A: Given that ,   y = c1ex + c2e-x  is  a solution of the differential equation y''-y =0. We have to…

Q: 1. Simplify the following numbers and write them in standard form: a. (4√-16+2 (150) -2(-4+3 (205)…

A: Given data 2+5i2-4i