22. Let f(x) = (x – 1)² g(x) = e-2x and h(x) = 1 + In(1 – 2x) (a) Find the linearizations of f, g, and h at a = 0. What do you notice? How do you explain what happened? (b) Graph f, g, and h and their linear approximations. For which function is the linear approximation best? For which is it worst? Explain.

Q: - (4y" + fy) = -A with y(-1) = -2, y(-1) = 1, y"(-1) = 0 Use x1 = y, x2 = y', and x3 = y". x + with…

A:

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: Suppose that g is a continuous function. Find the general solution of y" – y = g(t).

A:

Q: Two equivalent forms of the Chain Rule for calculating the de-rivative of y = f(g(x)) are presented…

A: Given, if y=fx and u=gx then the derivative of their composition can be expressed as

Q: 1. Suppose f(-2) = 3, f'(-2) =-4 g(3) = 2, g'(3) = -1 1.1. What is the linear approximation to k(x)…

A: Linear approximation formula is k(x)=k(a)+k'(a)(x-a) Formula of derivative of composition of…

Q: Suppose m and b are constants. What is the linearization of the function f(x) = mx + b at any given…

A: Given function f(x)=mx+b where m and b is constant our aim To evaluate linearization of f(x) at…

Q: Show that the linearization of ƒ(x) = (1 + x)k at x = 0 is L(x) = 1 + kx.

A: The given function is

Q: 1. Consider the function f(x, y) = -3 +4xy – 2y² +3. (a) Find all critical points (b) Classify these…

A:

Q: Suppose m and b are constants. What is the linearization of the function f(x) = mx +b at any given…

A: Givenf(x)=mx +b where m and b are constantsTo find linearization of f.

Q: 28. Find the critical points of f(x) = x3 – 3x2 - 3. а. (0,—3)аnd (2, -7) b. (0,3)and( 2,7) c. (0,2…

A:

Q: sider the general equation of a quadratic function: f(x)=ax2+bx+cf(x)=ax2+bx+c (Recall: aa, bb, and…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

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

A: Given, f(x)=1x, a=0.9 now find linearization f(0.9)=10.9=109 so linearization at 910,109…

Q: 1. A) Find the linearization of the function at the given point. f (x, y) = 2 + x In (4 – xy), at…

A: (NOTE- These are two completely different questions, only required to do the first one. Please post…

Q: 17. Suppose the radius r, height h, and volume V of a cylinder are functions of time t, and further…

A:

Q: Question 1 Find and classify the critical points of the function f(x, y) = y* – 2y² – x³ + 3x.

A: The given function is: f(x,y)=y4-2y2-x3+3x

Q: 4 Find the linearization of the function f (x) = x² at x = 1. L(x) = Using this linearlization, ƒ…

A: f(x)=x4 at x=1 So, L(x)=f'(1)(x-1)+f(1)

Q: Determine two functions, defined on the interval  ( − ∞ , ∞ ) , whose Wronskian is given by  W ( f 1…

A: To determine two functions having the prescribed Wronskian and decide on their linear independence

Q: Suppose that a consumer derives his utility from two goods, the amounts of which are x and y,…

A:

Q: Suppose that we were to model a continuous income stream using the function f(t)=t2 / (t-1)(t+1) for…

A: The function that models a continuous income stream is

Q: We have found the following Wronskians. W = -e-³x; W₁ =-e-2x(4+ex)-¹; W₂ = e¯x(4+ e*)-¹ We want to…

A:

Q: 11. Find the linear approximation of f(x) = √√x_ at a = 1. Use the linearization to estimate the…

A:

Q: 7  please answer, type the solution if you can please. or write clearly

A:

Q: fCx)=(1+x)* at X=0 is LUX)=1+ KX + "७) %3

A:

Q: 4) Find the critical points of the function f(x, y) =exp((−x3/3)+x−y2 ) and determine their type.…

A: Consider the given function.

Q: 4. A company possesses a major piece of equipment that denigrates at a continuous rate f = f(t),…

A: (a) Let F(t) be an antiderivative of f(s) Mathematically, it means: F'(s) = f(s) By Fundamental…

Q: 4. A company possesses a major piece of equipment that denigrates at a continuous rate f = f(t),…

A:

Q: In x Find the linearization of f(x) = xmª around x = e. Round the gradient and y-intercept, whenever…

A:

Q: 6. Consider the function f(1, y) = Suppose we would like to make small changes Ax and Ay to the two…

A:

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

A: The nearest integer to a=-0.9 is -1 because at this point, we can easily find the function's value…

Q: Find the Linearization L(x) of y= (3+ x)-1/2 at a = 1. L(x) =

A: To find the Linearization.

Q: find a point c satisfying the conclusion of the MVT for the given function and interval y = e−2x ,…

A:

Q: 2. Give an example of a regulated function f on [0, 1] such that f(x) > 0 for all æ e (0, 1), So…

A:

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

A: (1)Given:

Q: 2: The necessary condition for existence of the solution of the nonlinear equation x =g (x) in…

A: For any non linear function, to find the existence of its solution between an interval there should…

Q: Suppose that y = f(x) is differentiable at x = a and that g(x) = m(x - a) +c is a linear function in…

A: You have correctly answered the first part. I will straightway go to the second part.

Q: For the function f (x,y,z,w) with x, y, z, and w all functions of s, t, andr, write out the chain…

A: The function is fx,y,z,w x,y,z,w are functions of s,t,r.   Partial derivative of a function with…

Q: In x is 2. A relative maximum value of the function y = (C) (D) (E) none of these (A) 1 (В) e

A:

Q: (12) Find the local maximum, minimum and saddle points (if any) of the function f(x, y) = x3 – 3x +…

A: Local maximum or minimum of the function

Q: Suppose m and b are constants. What is the linearization of the function f(x) = mx + b at any given…

A: The given function is: f(x)=mx+bSo,f'(x)=m

Q: II- Find the local maximum and minimum values and saddle points of the 3y? 3xy - 2 function f(x, y)…

A:

Q: 1. Find any local maximum and minimum values and saddle point (s) of the function f(x, y) = -6xy +…

A:

Q: x+2 Find the linearization of f(x) = 6 - 21 dt at x=4. 1+t 6

A: Given a function f(x) at x=4 We have to find the linearization of f(x) at x=4 For solving this 1st…

Q: 1. Any function y = f(x) can be expressed as x = f(y) in standard mathematical methods for solving…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Find the absolute maximum and minimum values of f(x) = e * – 3x on [0,5].

A: f(x)=ex-3x Take derivative wrt to x f'(x)= ex-3

Q: 1. Determine the nature of the stable points of the function f (x, y) = x²y – x² – 3xy + 3x + 2y –…

A:

Q: Let y : R → R be the real-valued function defined on the real line, which is the solution of the…

A: The differential equation is given as Y’  = -xy + x , y(o) = 2 From the type of the problem we can…

Q: 1)Classify the critical points of the function f(x,y)=x²+y³+x²y+4

A:

Q: 9. An equation of the line normal to the graph of f(x)=, at (1,–1) is (a) 2x - y -3 -0 (b) 2x + y…

A: Explanation: Given that  f(x)=xx-2 at (1,-1)   Concept Used: To find the normal firstly find the…