3. Find the linearization function for the function f(r.y) = V? + y² + 2 about the point (-1. 1) and give the upper bound for the error when approximating f(-1.1, 1.1).

Q: find a linearization at a suitably chosen integernear a at which the given function and its…

A: Given that the function is  f(x)= e-x, a= -0.1 To determine the linearization for the function.  The…

Q: The linearization of ex at x = 1 Estimate to five decimal places the magnitude of the error involved…

A:

Q: Find the linearization L(x, y) of f(x, y) = x2 y3 at (a, b) = (2, 1). Use it to estimate f(2.01,…

A:

Q: The integrating factor of the LDE y' = x - 2ycotx is

A:

Q: 5Find the Orthogonal trajectories of the family of r=aeº

A: Question:- Find the orthogorial trajectories of the family of r=aeθ ?Solution :- We have r=aeθ -(i)…

Q: Find the local linear approximation to f(x) = Vx at x = 1 and use it to approximate both 1.1 and…

A: To know which one is better we have to compare with calculator values of sqrt(1.1)  and sqrt(0.1)

Q: 2ys = Cx

A:

Q: the linearization of (fi,f2) = (x²y+ 3xy², 3x³ + 2xy) at (1,0) to approximate the value at…

A:

Q: Find the linearization of the function f(x,y) = V9x² + 16y² at the point (1, 1), and use it to…

A:

Q: (6) Find the orthogonal trajectories of the family of curves r 4C cos 0, where C being %3D…

A: We have to solve given problem:

Q: Determine two functions, defined on the interval (−∞,∞)(−∞,∞), whose Wronskian is given by…

A:

Q: Find the linear approximation of f(x) = e(a) at a = 1.

A:

Q: (6) Find the orthogonal trajectories of the 3C cos 0, where C family of curves r being parameter.

A: Answer

Q: A:- Find the orthogonal trajectories for functions In -1) = - COS X +a y

A: The given family of curves is: lny-1y=-cos x+a ,            where a is an arbitrary constant.

Q: 7. Find the linear approximation near (2, 0) of f(x, y) = 3x e¯3ªy.

A: To find the linear approximation for the given function.

Q: Find the orthogonal trajectories of the family of curves xy = a where a ≠ 0is an arbitrary constant.

A: Consider the equation: xy=Cy=Cxy'=-Cx2 Substitute the value of C in the first derivative:…

Q: 4) Find the orthogonal trajectories of the family of the curves x² = 2y – 1+ ce¯2y.

A: We need to find the orthogonal trajectories of the family of the curve given by x2=2y-1+ce-2y We…

Q: 4) Consider the function 9 defined by g(x, y) = cas (7X Jj ) + logg(x-y) does 9 ha ve the maximum…

A: direction of maximum increase  Let maximum rate of change of a function f(x,y)  occur in the…

Q: (6) Find the orthogonal trajectories of the family of curves r = 3C sin 0, where C being parameter.

A: Orthogonal trajectory curve of a family of curve is defined as a curve which intersects every member…

Q: 8. What is the relationship between a and b so that F(x, y) = (ary, 3ax + bry) is source free?

A: That's easy. Have a great day!!!

Q: Find the derivative of the given function at P. (3, 3, 3) in the direction of u = 3i + 4j f (x, y,…

A:

Q: 4. Use the linearization of f(x, y) Vx + 2y to approximate f(3.01,2

A:

Q: Find the linearization of f(x) = 3+ S" sec(t - 1)dt at .2 END x = -1

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: 3. Find the interval on which the curve of y= 2 1+3t+t² dt is concave up.

A: Second derivative is positive.

Q: Find the linearization L(x)of the function at a .

A:

Q: Find the linearization of the function given below at the specified p f(x) = 4 In(x) at a = 1 L(x) =…

A:

Q: 18. Use the Linear Approximation to f(x, y) = /x/y at (9,4) to estimate 19.1/3.9.

A:

Q: Find the linear approximation to h(x) = Vx at x = 2. Use the linear approximation t approximate the…

A: Introduction: The linear approximation of a function at a given point is an application of…

Q: find the solution of following derivative by Runge-Kutta method f(x,y) = -2x3+ 12x2 - 20x + 8.5 let…

A: Consider an initial value problem dydx=f(x,y) with the initial condition yx0=y0. Then Runge-Kutta…

Q: Find an equation of the line tangent to f(x) = xcos x at x = -4. (Round coefficients to 3 decimal…

A:

Q: suppose that y is an implicit function f(x) defined by the equation x^3 + y^3 = 8xy − 7. find the…

A: suppose that y is an implicit function f(x) defined by the equationx3+y3=8xy−7. find the equation of…

Q: Find the best linear approximation to f on th e interval [0, 1].                            f (x)…

A:

Q: 3) Consider a particle of mass m in a one-dimensional box of width L. Apply the variational…

A:

Q: 5) Construct a linear approximation of the function f(x ) = lacX+s) about the point x,= 1. Compare…

A: Tangent line approximation or linear approximation is very significant in differential calculus.…

Q: Find the best linear approximation, g, to f on the interval [0, 1]. (x) = 2/x g(x) %3D

A:

Q: (4) Find the orthogonal trajectories of the family of curves z +y = 20C?, where C being %3D a…

A:

Q: Find the best linear approximation to f(x) = ex on the interval [-1,1]

A: We have to find the best linear approximation of f(x)=ex on the interval -1,1.

Q: What is the linear approximation for any generic linear function y=mx+b?

A: Given: y=mx+b

Q: 4x 28. If R = and errors in x, y, z be 0-001. Show that the maximum relative error at x = y = z = 1…

A:

Q: Find the linearization of the function f(x)=x5 at x=1. L(x)= Using this linearlization, f(1.04).is…

A:

Q: For the family x² + 3y2 = c, find that member of the orthogonal trajectories which passes through…

A:

Q: Integrate from f(x) = x4 from 0 to 1 by (Trapezoidal Rule) with h = 1, h = 0.5, h = 0.25 and…

A: Here, f(x)=x⁴ So, I=  Integrate from f(x) = x⁴ from 0 to 1. Now we can solve by Trapezoidal rule,…

Q: 4) Find the orthogonal trajectories of the family of the curves x² = 2y – 1+ ce¬2v.

A: Given information : Family of curves :  x2 = 2y -1 +ce-2y

Q: 5) a) Compute Ko for the function f0=V+X by using the de finition of the deniratire, b) Find the…

A:

Q: 9. Find the orthogonal trajectories to the following families of curves: x = ke¯v, where k is a…

A:

Q: determine the equation of the orthogonal trajectories of the following families curves: e^x+e^-y=C1

A:

Q: Find L(x) (Linearization function), given f(x) = ev2x at the value a = 2.

A:

Q: (6) Find the orthogonal trajectories of the family of curves r= 2C sin 0, where C being parameter.

A: See the detailed solution below.

Q: 8. Find the orthogonal trajectories of y cx

A:

Q: Find the orthogonal trajectories of the given family of curves x^2 + y^2 = c^2. *

A: Curves:  x²+y²=c²

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.