Find the linearization​ L(x) at x=a.   ​f(x)=−4x3−3x+1                                 a=−1   ​L(x)=

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

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Q: 3. Determine the differential coefficient of y + 2x - 3 when x = 7 %3D

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

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

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Q: Given the function y = x3 + x² + x + 10, suppose x increases from 1 to 1.1. Find the absolute error…

A: We will find out the required value of absolute and percentage error.

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: If y=-2x² + sin x solve for the differential of dy.

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Q: solve xdx+ydy=a^2(xdy-ydx)/(x^2+y^2) using exact Differential Equation

A: Given equation is x dx+y dy=a2x dx-y dyx2+y2.

Q: A population of insects grows at a rate that is given by dN = 0.078N dt - If there are initially 100…

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Q: (b) x" – 2x' + x = 4e'.

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Q: where y is considered to be a function of . In this exercise, you will determine whether or not y =…

A: The given differential equation is y' = y2. The objective is to determine whether the equation y =…

Q: Solve the following differential eyuation x 2+ 2y = x* e** y.

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

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Q: For the differential equation x ^ 2y ”+ xy’ + y = 0, check that y1 = cos (lnx) is a solution. Find…

A: According to the chain rule of differentiation, the differentiation of the composite function…

Q: Solve the differential equation xy' ==x + 3y, for x

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Q: dy/dx=x squre root of y for y doesnt equal 0 Solve the differential equation

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Q: Find the particular solution that satisfies the differential equation and initial condintion.…

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Q: Find a differential equation by eliminating the arbitrary constants A, B from the relation y= Ae²* +…

A: (a) The given relation is: y=Ae2x+Bxe2x...(1) To find a differential equation by eliminating the…

Q: Solve for homogenous differential equation (x + y)dx + 2xdy = 0

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Q: Most savings banks advertise that they compound interest continuously, meaning that the amount S(t)…

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Q: Solve the differential equation xy'+y = x^(8) ln x, given that when x=1, y=3. Solve for y.

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Q: Use the integrating factor to solve y' = -3a²y + sin(x)e-*, with y(0) = 1.

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Q: Given a differential equation (3x²y + 2xy + y³) dx + (x² + y²) dy = 0. What is the Integrating…

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

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Q: As a salt dissolves in methanol, the number x(t) of grams of the salt in a solution after t seconds…

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Q: verify that the indicated function is an explicit solution of the given differential equation…

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Q: 15. x" + x = tan t; x=-(cost) In(sect + tant)

A: Given, x''+x=tant x=-costlnsec(t)+tan(t)x''=cos(t) ln(tan(t)+sec(t))+tan(t)

Q: Given the differential equation  (ye^-x -sinx)dx -(e^-x +2y) dy = 0, what is the value of f'(y)?

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Q: For which value(s) of r is y = x" In(x) a solution of the differential y (3 In(x) + In(x)

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Q: The intensity L(x) of light x feet beneath the surface of the ocean satisfies the differential…

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Q: For the given non exact differential equation, determine the integrating factor. (x2 + 2xy - y2) dx…

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Q: The proportion of people in a community infected with a virus that stays active for two weeks is x…

A: The complete solutions are given below

Q: 5. Verify that y = (x³ – x) log cx satisfies the differential equation (x³ – x)y' – (3x? – 1)y = x5…

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Q: what is the differential coefficient of x.

A: To find differential coefficient of x we need to differentiate x with respect to x.

Q: Use the method of undetermined coefficients to solve the differential equa- tion: y" – 2y' + 2y =…

A: Here by using the method of undetermined coefficients we have to solve the given differential…

Q: Find the general solution of the differential equation using any method         y′ = ln(x2 + x)

A: we have to find the solution of the given differential equation  y′ = ln(x2 + x)

Q: Solve the initial-value problem by using integrating factors. xy' = y + 4x ln(x), y(1) = 3

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Q: 1 Solve for the differential of y when y=sinzx, x=÷, and dx= - 3 A) B) 2 -- C) D)

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Q: It is estimated that t years from now, the population of a certain town will be F(t) = 40-{8/(t+2)}.…

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Q: -SOLVE THE DIFFERENTIAL EGQUATION (xty) dx +(2xy + xIn 3v ) du-0 WHEN X Y=2

A: The given problem is to solve the given differential equation with given initial condition, we have…

Q: Solve for the differential equation: dy/dx - ytan x = cos x

A: To find the solution of the linear differential equation of first order y'+Py=Q, where P and Q are…

Q: Find the particular solution to the differential equations,Evaluate the polynimial by finding the…

A: Given that: xdy+ydx+xy(3dx+dy)=0x=-3 and y=9

Q: 8. Obtain the differential equation associated with the given function: y = Cx² + C².

A: Proceed as shown

Q: 1 Solve for the differential of y when y=sinx, x=÷, and dx=-

A: Solution. A is true.

Q: Verify x = e + 2te' satisfies the differential equation [2 x' = 3 x+e

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Q: Solve for the differential of y when y- sinax. x= and dx O o o

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Q: 10. Give the differential of f(x) =x² - 3x at x = 1 with respect to the increment 1/10. 11. Use…

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Q: Find the value of n such when the differential equation (x + y3)dx + 6xy2dy = 0 is multiplied by xn…

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Q: Find the general solution to the given differential equation. (Use C for the constant of…

A: Given,         dydx=x5y

Q: Given the linear differential equation: y'' - y = cos(x) - 5sin(2x) Find the general solution…

A: Solving