Find the linearization of the function at a. 1. f(x) = x^4 + 3x^2, a = -1 2. f(x) = sin x, a = pi/6

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A: The solution for the above question is as shown below.

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A: 1 st we need to get general equation of all circle whose center lie on the given line. Now use…

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A: This is a simple question based on differential equations which could be solved using the basic…

Q: 2. Find the differential equation of the family of curves as described below. a. Family of circles…

A: As you asked multiple question I solve only the first one 2.a) We have to find out the differential…

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A: Note:- As per our guidelines, we'll answer the first problem as exactly one is not mentioned. Please…

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Q: Obtain the differential equation of the family of circles of fixed radius r with center on the…

A: We have to obtain the differential equation of the family of circles of fixed radius r with center…

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A: The general equation for a circle can be written as

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Q: Obtain the differential equation of the family of curves described and sketch some members of the…

A: We will find differential equation of the given condition.

Q: Obtain the differential equation of the family of curves as described. Draw some representative…

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Q: 5. Obtain the Differential Equation from the family of vertical parabolas whose vertex is at (h,k).

A: Formation of the differential equation

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Q: Find the derivative of y = 4) G* eln sin-) y = G (In-x) sin + V4 – x2. x sin¬1 In sin + (Tx-1 1 y' =…

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Q: Obtain the differential equation of the family of curves described and sketch some members of the…

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Q: find the differential equation for the following families of curves. 8. Horizontal parabolas whose…

A: Consider horizontal parabolas whose vertices lie on y-axis. The objective of the problem is to find…

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Q: Find the differential equation of family of circles tangent to the x-axis.

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Q: The function y(x) is defined by the implicit equation x2−√ylny=1. Find its differential at the point…

A: Differentiate both sides with respect to x and solve for dy/dx

Q: Find the Differential Equation of the family of circles with center on the line y = x, and passing…

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Q: 7. Find the differential dy of the function y = x (1-cos(x)). If the error in x is ", find the error…

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Q: obtained in factored form a linear differential equation with real constant coeffiecients that…

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Q: 3. The sum of the lengths of the two diagonals of a parallelogram is 18 m. One diagonal is 2 meters…

A: Here we will use two formula  1st Area of triangle  If two sides of a triangle has length a and b…

Q: Find the differential equations of the families of curves. 1.) Straight lines with slope and…

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Q: Obtain the differential equation of the family of curves described and sketch some members of the…

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Q: Obtain the differential equation of the family of curves described below. a. Circle of radius 1 and…

A: a) Given radius of circle r= 1 and center lies on y=x linewe know that circle equation is…

Q: Find the differential of the given functions. 1. y= x-2x² + 5 5. у 3 1- -s2

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Q: Find the general antiderivative of each function. (can check by taking the derivative) F(X)= 12x3…

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Q: Suppose f is differential equation on (-inf, +inf), f(3)=12 and f'(3)=-2 use linear approximation to…

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Q: Obtain differential equation of the family of curves with properties indicated

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Q: Suppose that a hare starts at the origin (0, 0) and runs with speed Vh along the y-axis toward a…

A: This question is from differential equation.

Q: Obtain the differential equation of the family of curves described and sketch some members of the…

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Q: Obtain the differential equation of the family of curves described and sketch some members of the…

A: Each part is independent of each other so according to the guideline , I am solving only first part…

Q: Find a differential equation of the family of circles with center on the line y = -x, and passing…

A: Let, the equation of the family of circles with center         on the line y=-x & passing…

Q: If the family of curve has 3 arbitrary constants then the corresponding differential equation is a)…

A: See solution below

Q: Find the differential equation of All parabolas whose axis is parallel to the y-axis. Draw at least…

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Q: 2. Obtain the differential equation having the solution as the equation representing all circles of…

A: The solution is given as

Q: Circles with center on the line y = x

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Q: Obtain the differential equation of the family of curves as described. Draw some representative…

A: Here first we write one parameter family of given curve and then we use differentiation to eliminate…

Q: 2) Obtain the differential equation of parabolas with vitex and focus on the x-axis

A: To find: the differential equation of parabolas on the x- axis.

Q: Find the differential equation of family of parabolas with axis parallel to the x-axis and with…

A: The general equation of family of parabolas with axis parallel to the x-axis, with a vertex at a…

Q: 27. Obtain the differential equation having the solution as the equation representing all circles of…

A: The differential equation of all circles of radius 1 and centers on  y=x

Q: Find y(1) for y" = - 4z - 4y, X, = 0, yo = 0, z, = 1, with step length 0.1 using Euler method (2nd…

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Q: SOLVE FOR THE DIFFERENTIAL EQUATION OF THE GIVEN FAMILY OF CURVES. 1. Parabolas with vertex and…

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