Linear Approximation Example Problems

Worksheet 17 Linear Approximation and Applications For each of the following, use a linear approximation to the change in the function and a convenient nearby point to estimate the value

In these cases we call the tangent line the linear approximation to the function at x a x a. So, why would we do this? Let's take a look at an example. Example 1 Determine the linear approximation for f x 3x f x x 3 at x 8 x 8. Use the linear approximation to approximate the value of 38.05 8.05 3 and 325 25 3.

Here is a set of practice problems to accompany the Linear Approximations section of the Applications of Derivatives chapter of the notes for Paul Dawkins Calculus I course at Lamar University.

Finding a local linear approximation at a given point is finding the equation of the tangent line at that point. a Find the local linear approximation of f x x3 - 2x 3 at the point where x 2.

Learn how to use Local Linear Approximation or Tangent Line Approximation, as a way to accurately estimate another point on the curve.

A collection of Calculus 1 Linear Approximation and Differentials practice problems with solutions

Time to practice! This screen has a series of practice problems for linear approximations, so you can develop your skills that we introduced on the preceding screen. As you work through the questions

Problems on linear approximations Using a linear approximation of a function about a point p to approximate the value of the function at a point q is only a good idea when q is close to p. Unfortunately, this is a vague statement because quotclosequot does not have an absolute meaning. Define a function for which the linear approximation about x0 provides a good approx-imation within 1 to

Example The natural exponential function f x ex has linear approximation L0x 1 x at x 0. It follows that, for example, e0.2 1.2. The exact value is 1.2214 to 4 d.p. Localism The linear approximation is only useful locally the approximation f x Lax will be good when x is close to a, and typically gets worse as x moves away from a.

This section contains lecture video excerpts and lecture notes on linear approximation, a problem solving video, and a worked example.