# Calculus tutorial

Types of Infinity — In this section we have a discussion on the types of infinity and how these affect certain limits. As we will see in the next section this problem will lead us to the definition of the definite integral and will be one of the main interpretations of the definite integral that we'll be looking at in this material.

We work quite a few problems in this section so hopefully by the end of this section you will get a decent understanding on how these problems work.

Also exercises with answers are included at the end of the page.

### Calculus problems

Not long ago, reading and writing were the work of trained scribes. Minimum and Maximum Values — In this section we define absolute or global minimum and maximum values of a function and relative or local minimum and maximum values of a function. Calculus showed us that a disc and ring are intimately related: a disc is really just a bunch of rings. Included in the examples in this section are computing definite integrals of piecewise and absolute value functions. In particular, there are prepared versions of these lessons as executable worksheets right on CoCalc! Implicit differentiation will allow us to find the derivative in these cases. Logarithmic Differentiation — In this section we will discuss logarithmic differentiation. Accumulate over time?

Area and Volume Formulas — In this section we derive the formulas for finding area between two curves and finding the volume of a solid of revolution. The integrals in this section will all require some manipulation of the function prior to integrating unlike most of the integrals from the previous section where all we really needed were the basic integration formulas.

Because we expect it.

## Calculus 1 syllabus

The Shape of a Graph, Part II — In this section we will discuss what the second derivative of a function can tell us about the graph of a function. Finding Absolute Extrema — In this section we discuss how to find the absolute or global minimum and maximum values of a function. Then you can get a copy of the files from here! But does it work in theory? We will cover the basic notation, relationship between the trig functions, the right triangle definition of the trig functions. Linear Approximations — In this section we discuss using the derivative to compute a linear approximation to a function. A note on examples Many calculus examples are based on physics. Solving Trig Equations — In this section we will discuss how to solve trig equations. Higher Order Derivatives — In this section we define the concept of higher order derivatives and give a quick application of the second order derivative and show how implicit differentiation works for higher order derivatives.

We will actually start computing limits in a couple of sections. Properties of Limits in Calculus. The Shape of a Graph, Part I — In this section we will discuss what the first derivative of a function can tell us about the graph of a function.

Implicit differentiation will allow us to find the derivative in these cases. More importantly, however, is the fact that logarithm differentiation allows us to differentiate functions that are in the form of one function raised to another function, i. You should always talk to someone who was in class on the day you missed and compare these notes to their notes and see what the differences are.

The only difference is that the answers in here can be a little messy due to the need of a calculator.

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