# Calculus sketch

Synopsis[ edit ] During a thunderstormglass and porcelain items at Marlinspike Hall shatter inexplicably. Insurance salesman Jolyon Wagg arrives at the house, annoying Captain Haddock. Gunshots are heard in the Hall's grounds, and Tintin and Haddock discover a wounded man with a foreign accent who soon disappears. The next morning, Professor Calculus leaves for Geneva to attend a conference on nuclear physics.  Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device should be able to scroll to see them and some of the menu items will be cut off due to the narrow screen width.

Functions of Several Variables In this section we want to go over some of the basic ideas about functions of more than one variable.

## Curve sketching with calculus: polynomial (video) | Khan Academy

This is an elliptic paraboloid and is an example of a quadric surface. We saw several of these in the previous section.

 Calculus I - Related Rates We ended up with — 5 x0 in the second term of the function by assuming the exponent in -5x could be written as -5x1, so we multiply it by the coefficient in front of the x, which is Calculus III - Functions of Several Variables Arrhenius equation and reaction mechanisms Video transcript - Let's see we have a zero order reaction where A turns into our products and when time is equal to zero we're starting with our initial concentration of A and after some time period T, we would have the concentration of A at that time.

We will be seeing quadric surfaces fairly regularly later on in Calculus III. We have a convention for graphing planes that will make them a little easier to graph and hopefully visualize.

This triangle will be a portion of the plane and it will give us a fairly decent idea on what the plane itself should look like.

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We next want to talk about the domains of functions of more than one variable. Now, if we think about it, this means that the domain of a function of a single variable is an interval or intervals of values from the number line, or one dimensional space.

Example 1 Determine the domain of each of the following. There is one for each square root in the function. Here is the sketch of this region. Here is a sketch of this region.

The next topic that we should look at is that of level curves or contour curves. Sketch a few of them. Note that this was not required for this problem.

It was done for the practice of identifying the surface and this may come in handy down the road. Now on to the real problem. We can graph these in one of two ways. We can either graph them on the surface itself or we can graph them in a two dimensional axis system.

The contour will represent the intersection of the surface and the plane. The final topic in this section is that of traces. In some ways these are similar to contours. Below are two graphs. On the right is a graph of the surface and the trace that we are after in this part.Given a function sketch, the derivative, or integral curves Use the language of calculus to discuss motion Explain what the effect of a discontinuity in a function has on the derivative and the integral curves.

Level 3 Calculus What's it worth? Students solve differential equations to find functions to model the value of a car in terms of its age.

## Increase your sense of wonder.

Then they compare their results with real data. Calculus has the reputation of being one of the most challenging subjects in school, even when compared with other advanced math classes.

That’s because calculus is usually the first exposure students get to a version of math that requires more than just memorization to succeed. AP Calculus – Final Review Sheet When you see the words .

This is what you think of doing 1. Find the zeros Find roots. Set function = 0, factor or use quadratic. Opening the Notebook. Let us start at the beginning. The notebook has two front covers. Einstein wrote in it in both directions.

There is the front cover shown above and first here. Calculus I. Here are the notes for my Calculus I course that I teach here at Lamar University.

Despite the fact that these are my “class notes”, they should be accessible to anyone wanting to learn Calculus I or needing a refresher in some of the early topics in calculus.

Propositional calculus - Wikipedia