Find the area of the shaded region. NO y=0 2 2 y = x^3 - 4x^2 6 8 HH 10

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A: We use ratio test to find the interval of convergence.

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A: Given x = - 6t - 3 & y = 5t + 2

Q: 2.5 2x dx 9-x²-8x

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

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Q: Use integration by parts to find the integral. (Use C for the constant of integration.) [x² In(ax)…

A: We have, ∫ xnlnax , where a ≠0 , n≠-1

Q: Find the given vector. 1. e, where v = (4, -2, -1).

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: Suppose a company has fixed costs of $400 and variable costs per unit of x + 1350 dollars, where x…

A: Suppose a company has fixed costs of $400 and variable cost per unit of  1516x+1350 dollars, where x…

Q: Consider the following differential equation to be solved by the method of undetermined coefficients…

A: According to question,Given differential equation,y''-2y'+10y=ex cos3x

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A: ∫xcosxdx

Q: (4) Suppose V(t) represents the volume (in gallons) of water in a tank at time t, where t is the…

A: Given: Suppose V(t) represents the volume (in gallons) of water in a tank at time t, where t is the…

Q: Please solve this 100% Correctly and ASAP. Thx  Find the equation of the tangent to the function y =…

A: Tangent line formula passing through the point (a,b) and slope m is  y-b=m(x-a)

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A:

Q: If you want to earn 7% annual simple interest on an investment, how much should you pay for à note…

A: A = P (1 + rt) Where  A -  Accumulated amount              P -  Principal amount              r -…

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: f(x) = 8+x 8 - x on [4, 6].

A:

Q: Use the chain rule to find əz Əs z = (x - y)², x = s²t, y = st² дz at = and az z =…

A: ∂z∂s = ∂z∂x×∂x∂s using chain rulewhere∂z∂x is partial differentiation of z with respect to x keeping…

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A:

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: The growth of a colony of bacteria can be described by exponential growth. If the colony initially…

A: Pt=P0ert⇒P0=initial population⇒r=Growth rate⇒Pt=Population at time t⇒t=time in hours

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A: The population of a city is modeled  by the equation  P( t ) = 479442e0.1t Where t is measured in…

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Q: The marginal profit is given by MP= P'x = x(90x+2x^2). Find the total profit function.

A: To find the total profit function, we need to integrate the marginal profit function with respect to…

Q: Consider the function are true? 1. lim f(x) = 70 II. lim f(x) = 70 III. lim x) = 100 X-8 IV. lim x)…

A: Given function f( x ) = 100 - 12000400 + 3000axWhere a < 0 < 1

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A: dθdt=0.1 rad/min In ∆ABC…

Q: Solve the given differential equation by separation of variables. (ex + 1)²e-y dx + (ex + 1)4e¯x dy…

A: ey+12e-y dx + ex+14e-x dy = 0

Q: Graph a vector, opposite to the given vector, that has an initial point at the origin. 02 PENCIL…

A: Let r is the given vector.We can see that given vector is passing through the point (-7,2) and…

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Q: This problem is represented by the following system: 3x +9y+22=98 8z + 5y +32= 105 4z +10y+z=100…

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Q: (3) Find the equation of the line tangent to f(x)=√x atx=4

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Q: 1/3 The integral fo²³ 3-√2-9x1² dx is to be evaluated 0 directly and using series approximation. 1)…

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Q: дz дz Use the chain rule to find and მs at z = ln(3x + 4y), x = s sin(t), y = t cos(s) дz as дz at…

A: z=ln3x+4y , x=s sint , y=t coss

Q: for each question. A correct answer without an explanation will not earn any credit. The population…

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Q: Suppose that the marginal revenue for firefighting protective clothes is MR = 258 - cost is MC =…

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Q: The rate (in liters per minute) at which water drains from a tank is recorded at half-minute…

A: The rate at which water drains from a tank is recorded at half minute intervals ∆t=0.5

Q: 2π A sector of a circle has a diameter of 8 feet and an angle of Round your answer to four decimal…

A: We have, θ = 2π/3  Diameter (2r) = 8 r = 8/2 = 4

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Q: An isotope of sodium has a half-life of 20 hours. Suppose an initial sample of this isotope has mass…

A: Given that the half-life of an isotope of sodium is 20 hours.

Q: 5. Determine a vector equation of the line that passes through the origin and is parallel to the…

A: Determine a vector equation of the line that passes through the origin and is parallel to the line…

Q: Q5 Use the graphs below to fill in blank for Q(5.1)-Q(5.6). Write DNE" for Does Not Exist" or NEI"…

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Q: Consider a right triangle with a side of length opposite angle A, a side of length y opposite angle…

A: Given: Consider a right triangle with a side of length x opposite angle A, a sideof length y…

Q: 1a Differentiate the following functions with respect to t and simplify your answer as far as…

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Q: 10 a) Find the simplified form of the difference quotient for the function f(x) = b) Complete the…

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

Q: (a) To buy a Treasury bill (T-bill) that matures to $10,000 in 6 months, you must pay $9780. What…

A: Given, To buy a Treasury bill (T-bill) that matures to $10,000 in 6 months, you must pay $9780. Then…

Q: 3. The following equation relates to how an investment will grow over time given an initial amount…

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Q: Find f(x) by solving the initial value problem. 5 f'(x) = 1 +e²+ = f(1) = 7+e f'(x)=1+e*+

A: Given: f'(x)=1+ex+5xf(1)=7+e We are required to find: f(x)

Q: Fast pls solve this question correctly in 5 min pls I will give u like for sure Sub a drinking cup…

A: Let’s solve this problem using calculus. Let’s say the radius of the cup is r and the height is h.…

Q: Find a function f(x, y, z) such that V f = (8z, 4y³, 8x). (Use symbolic notation and fractions where…

A: Given that :-       ∇f=8z,4y3,8x  ⇒∇f=8zi^+4y3j^+8xk^  ....(1) Now we know that…

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

A: Consider the region bounded by the parabolas:  y=x2+4x+3 and y=-x2+2x+3 To calculate the volume of…