Linearazationish Problem

• PsychonautQQ
In summary, the conversation discusses the comparison between Δz and dz, with Δz being the difference between two values of z and dz being the differential of the function z. The question asks for a comparison between the two values, and it is suggested to try the difference of both initial and final values.

Homework Statement

If z=x^2-xy+3y^2 and (x,y) changes from (3,-1) to (2.96,-.95) compare the values of Δz and dz.

The Attempt at a Solution

So I plugged the two given sets of (x,y) into and solved for z and subtracted one from the other and got |.7189|. I don't know what the question means when it says compare it to dz. Since z is a function of two variables how do I do this? To I take the partial with regards to each variable or whaaat? does anyone know what the question is asking?

so I took the function partial of x and added it to the partial of y. it wants me to compare delta_z with dz. Which numbers should I plug in for dz? The initial values or final?

Try the difference of both!

1. What is a linearizationish problem?

A linearizationish problem is a mathematical problem that involves finding a linear approximation to a nonlinear function. This is often done to simplify the problem and make it easier to solve.

2. How is a linearizationish problem solved?

A linearizationish problem is solved by first finding the derivative of the given nonlinear function. Then, the linear approximation is found by substituting the derivative at a specific point of interest in the function.

3. What are the applications of linearizationish problems?

Linearizationish problems are commonly used in physics, engineering, and economics to approximate nonlinear phenomena. They are also used in optimization problems to find the maximum or minimum of a function.

4. What are the benefits of linearizationish problems?

Linearizationish problems allow for the simplification of complex nonlinear functions, making them easier to analyze and solve. They also provide a good approximation to the original function, making them useful in various real-world applications.

5. Are there any limitations to linearizationish problems?

Linearizationish problems are only accurate for small intervals around the chosen point of approximation. They also do not provide an exact solution to the original nonlinear function, but rather an approximation. In some cases, this may not be sufficient for certain applications.