Find the linear approximation of f(x) = (1 +x)" at x = 0. Use this approximation to estimate (1.01)³ %3D

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A: This question is based on average rate of change of function.

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A: Rate of increase of population  of insects  dPdt = 260 + 6t + 0.3t2 per day

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A: Given question:- What is the difference between the linearization, L(x), of f at a, and the linear…

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A: To find the derivative of given integral.

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Q: Find the average rate of change of g(r) = 5x - 1 from z - 2 to z = 1 =D1 =

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Q: What is the average rate of change of the function k(x) = 5x– 11 over the interval -asrs? -22 Sx?

A: Dear students here I'm answering to this problem according to our company guidelines so, here I can…

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Q: The total derivative of f(x,y )=3 x+ 3 y-41n y is

A: Given function is fx,y=3x3+3y2-4 ln y find the total derivative  dz=fxx,ydx+fyx,ydy

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Q: A 200-gal tank is half full of distilled water.At time t = 0, a solution containing 0.5 lb / gal of…

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Q: Find the linearization of the function k(x) = ln(x) when x= 1 and use it to estimate ln(1.1).

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Q: What is the result of integrating a population growth rate betweentimes t = a and t = b, where b…

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Q: Find the average rate of change of g(x)=4x^4+8/x^3 on the interval [-1, 1].

A: Average rate of change formula is  g(b)-g(a)b-a Where [a,b] is the given interval Given interval is…

Q: Estimate the instantaneous rate of change of the function f(x)=2x^2−1 at x=1 using the average rate…

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Q: Consider a tank that initially contains 100 gallons of a solution in which 50 pounds of salt are…

A: Here I am attaching image so that you understand each and every step.

Q: Let y=sin(5x)y=sin(5x). If Δx=0.1Δx=0.1 at x=0x=0, use linear approximation to estimate Δy and find…

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Q: The half-life of a radioactive material whose rate of disintegration is proportional to the amount…

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Q: Rank the functions x3, ln x, xx, and 2x in order of increasinggrowth rates as x→ ∞.

A: Given x3, ln x, xx, and 2x

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Q: What is the integrating factor of y' - 2xy x?

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Q: Use f(x+0.0001)-f(C) 0.0001 f(x)=52²-7x ata = 2, to the nearest tenth. to determine the…

A: Given function f(x)=5x2-7x

Q: Consider the function E(x)=x2+6x-5. Compute the average rate of change of E(x) over the interval [a,…

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Q: Find the average rate of change of g(x) = 4x° – 1 from x = - 1 to x = 1

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Q: Find a formula for the average rate of change of f (x) = x^3 over [2, x] and use it to estimate the…

A: We use the average rate of change formula

Q: Confirm the approximations by using the linear approximation at x = 0

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