Given f(x) = 8x3 + In(x – 1). Estimate the value of f(2.01) using differential. %3D

Q: For what value of x will the curve y = x3 – 3x2 + 4 be concave upward?

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Q: Use the method of undetermined coefficients to solve the differential equa- -2x y" + 5y' + 6y = e-®…

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Q: What is the amount of salt in the tank at time t = 0?

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Q: Let the rate of growth dN/dt of a colony of bacteria be proportional to the square root of the…

A: Let N(t) denotes the number bacteria present at time t. Use the proportionality constant k, to get…

Q: (a) Apply first principles, to calculate the differential coefficient of (x) = 5(3x²+2) when x = 3.

A: Solution a: Given function is f(x)=5(3x2+2) using first principle…

Q: x-1, X)1 find the generol solution of the differential eguation below

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Q: OFind the second derivative of y = 4Vx + E + 10

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Q: A company will sell N units of a product after spending $x thousand in advertising, as given by N =…

A: We are given that N=50x-x2, 5≤x≤25. Now, dN=50-2x dx. First, increase the advertising budget from…

Q: For what values of r does the function y= e™* satisfy the differential equation y"- 4y'+ 2y = 0?

A: for the homogeneous differential equation, the auxiliary equation is  compare this equation with…

Q: Solve the differential equation Integrating Factor by Inspection: xdy – ydx = 3x²(x² + y²)dx

A: We have to solve the differential equation xdy-ydx=3x2x2+y2dx by using integrating factor by…

Q: What is the value of the differential if f(x) = x + 2x - ! x = 8.4 and dx = 0.86. Round your answer…

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Q: Use differentials to estimate the value of V1.3. Compare the answer to the exact value of V1.3.

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Q: Solve the differential equati on. dz (log x) = –(log z) dx X

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Q: Find the differential of the function. z = 3t - = zp

A: Differentiate the function: - Differentiation is that the quantitative relation of a small amendment…

Q: Solve this differential equation using power series: y''+y=kx^2 where k is a constant.

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Q: Find the approximate height of the curve y = x3 – 2x2 + 7 at the point where x = 2.98. (SOLVE BY…

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Q: Solve the differential equaton 2x2dy=(x+y)2dx

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Q: Find the differential of the function y = f(x) . f(x) = (5x² + 7)/3 dy =

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Q: A population of insects increases at a rate of 260+6t+0.3t2 insects per day. Find the insect…

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

Q: If  f '(x) = x4,  what is f(x)? (Use C for the constant of integration.)

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Q: Find the total derivative dy dw. Y=3x+2w+5z x=4 In(w*) z=e43x³

A: Given, y=3x+2w+5z2x=4ln(w2)z=e-z+3x-3

Q: Jesaki Inc will sell N units of product after spending $x thousand in advertising, as given by N =…

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Q: Is the differential equation x" + e^x - 1 = 0 conservative or non-conservative? Explain why? If it…

A: Given x''+ex-1=0

Q: 3x =2 when x= What is the particular solution to the given differential equa

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Q: For what function P is the integrating factor α(x) equal to x?

A: We know that , integrating factor of the differential equation is

Q: Given that X ~ Exp(0.7), find the decay rate.

A: Given that X ~ Exp(0.7).

Q: Assume that the rate of evaporation for water is proportional to the initial amount of water in a…

A: Here, given that rate of change of evaporation is proportional to the initial amount of water.…

Q: Use variation of parameters to solve the differential equation x²y" + 10xy' + 8y = x².

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Q: Use variation of parameters to find the general solution of the differential x²y" - 5xy' + 5y = 4x…

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Q: If f'(x) = 5x*, what is f(x)? (Use C for the constant of integration.) f(x) =

A: To find the integration

Q: Solve the differential equation Integrating Factor by Inspection: xdx + ydy = (x² + y²)dx

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Q: Solve the differential eqution y'-y=7e^x

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Q: Suppose that electricity is draining from a capacitor at a rate that is proportional to the voltage…

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Q: The monthly output of a certain product isQ(x) = 2400x5/2where x is the capital investment in…

A: The monthly output of a certain product is Q(x) = 2,400x5/2, where x is the capital investment in…

Q: g) For how long do we have to invest $1000 at a rate of 2.5% compounded continuously to obtain a…

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Q: Find the differential of the function f(x) = (x+4)^(1/2) dy =

A: Find the differential of the functionf(x) = (x+4)^(1/2)

Q: Find the linear approximation of f(x)=ln x at x=1 and use it to estimate ln(1.24). L(x)=?…

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Q: -X y" + 2y² + y = €²² ln x e^

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Q: - ydx + (x ++xy )dy= 0

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Q: To use differentials to approximate V8. You would use x = and dx

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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: The mass of a radioactive sample is given by M(t)=M010^-kt where t is the time in years, M0 is the…

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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: Solve the ordinary differential equation (ODE) dxdt=5x−3 for x(t).

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Q: 17 It is found that the bloodstream concentration, C (in ug/mL), can-be modeled by C(r) T2 + 11…

A: According to the our guidelines we are supposed to do only first three subparts. Kindly repost the…

Q: Given the function y = x3 + 7x, find the differential dy.

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Q: Find a differential operator that annihilates the given function. xe3xsin5x

A: given function is                                                      f(x)=xe3xsin5x we have to…

Q: x (xdx + ydy) + y (xdy – ydæ) = 0

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Q: What is the value of the differential if f(x) = x + 2x - x = 2 and dx = 0.63. Round your answer to…

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Q: If y = 5x2 + 2x + 9 , find the value of the differential dy as x changes from 3 to 3.1

A: Given, y = 5x2 + 2x + 9Differentiating with respect to x;dydx = 10x + 2At x = 3, dydxx = 3 = 10×3 +…