 # How To

Introduction
The How To video series is a collection of videos recorded by the Math Learning Center tutors solving common math problems. This is a good resource for learning how to solve new problems or as a refresher for material you may have learned in the past.

Each How To page is listed below, and you can read the description to see what types of examples are covered. Also, you can view the video playlists to see more detail and click a playlist to go straight to those videos.

Note that each page has a recommended level corresponding to a particular math course. You do NOT need to be in that course, but this does give you an idea of the difficulty and mathematical rigor of the examples on that page.

Precalculus
Recommended Level: MATH 150

### Algebra, Functions, Linear Systems, Vectors, Trigonometry

This page covers topics from precalculus topics such as lines, rational functions, functions, the difference quotient, vectors and systems of equations. It also includes exponentials, logarithms, and trigonometry.

Video Playlists 3 videos Equations of Lines Writing the different forms for the equations of a line given two points on the line 3 videos Factoring Factoring polynomials 8 videos Rational Functions Performing operations with rational expressions and finding the holes and vertical asymptotes of rational functions 4 videos Roots of Functions Finding the roots of functions 13 videos Functions: Domain, Composition and Inverses Finding the domain and inverse of common functions and finding the composition of two functions 3 videos Difference Quotient Finding the difference quotient and simplifying your answer 5 videos Solving Inequalities Using a sign diagram to solve inequalities 2 videos Properties of a Quadratic Writing a quadratic in standard form and determining its absolute maximum or minimum 4 videos Vectors Calculating vector operations and the dot product and finding a unit vector 5 videos Systems of Equations Solving systems of linear equations and systems including a quadratic equation 9 videos Exponential Functions Solving equations with exponential functions, modeling population size and finding the horizontal asymptote 9 videos Logarithmic Functions Using properties of logarithms, finding the vertical asymptote, and solving equations with logarithmic functions 13 videos Trigonometry Evaluating trigonometric and inverse trigonometric functions, solving trigonometric equations, and graphing trigonometric functions

Calculus 1
Recommended Level: MATH 142

### Limits, Derivatives, and Applications of Derivatives

This page gives an introduction to limits including limits at infinity and infinite limits. It also covers calculating derivatives and using the common derivatives rules such as the Product, Quotient, and Chain Rule. Lastly, it includes applications of derivatives such as related rates and using the derivatives to graph a function.

Video Playlists 6 videos Introduction to Limits An introduction to evaluating limits using graphs, numerical approximation, and substitution 11 videos Limits: At Infinity and Infinite Solving limits at infinity and limits that may have infinite behavior 5 videos Continuity Determining where functions are continuous algebraically and using graphs 6 videos Average and Instantaneous Rate of Change Finding the average and instantaneous rate of change and the slope of secant and tangent lines 3 videos Limit Definition of the Derivative Using the limit definition to find the derivatives of functions 20 videos Calculating Derivatives Finding derivatives of common functions and using the product, quotient and chain rules with several business applications 6 videos Implicit Differentiation and Related Rates Finding derivatives with implicit differentiation and logarithmic differentiation and solving related rates problems NEW! 7 videos Analyzing Graphs with Derivatives Finding critical values, extrema, and inflection points; finding intervals where the function is increasing or decreasing and concave upward or downward NEW! 7 videos Absolute Extrema and Optimization Finding the absolute maximum and minimum on closed intervals; solving word problems by optimizing functions with given constraints NEW! 28 videos Antiderivatives and Integrals Finding antiderivatives of functions and solving indefinite integrals including examples using $$u$$-substitution; estimating area under curves with Riemann sums; finding the average value of a function; finding the area between curves