Intuitive Calculus Blog
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The Intuitive Calculus Blog keeps you up-to-date with all additions and changes to the intuitive-calculus.com Web site. Subscribe here.en-uscalculusWed, 9 Nov 2016 14:02:56 -0500Wed, 9 Nov 2016 14:02:56 -0500intuitive-calculus.comThe First Derivative Test: Intuition and Examples
http://www.intuitive-calculus.com/first-derivative-test.html19c5ce69354ac879cb45b17d75c212aeThe first derivative test is one of those ideas that confuses almost every student learning calculus for the first time. Here we'll learn the intuitive idea behind this test...Thu, 16 Oct 2014 08:23:16 -0400Critical Points of a Function: Intuition and Examples
http://www.intuitive-calculus.com/critical-points-of-a-function.html8cb708692f2567a043c2c78134533281Let's talk about critical points of a function. In this page I'll show you the intuition behind this concept and we'll go over a lot of examples on how to find them...Mon, 13 Oct 2014 07:56:43 -0400A Complete Guide to the Essential Calculus Problems
http://www.intuitive-calculus.com/calculus-problems.html829faa030ab80ef057f79de529290a75The Calculus Problems Manual contains the essential exercises you need to know how to solve to get an outstanding grade in a calculus course.Thu, 2 Oct 2014 09:48:26 -0400Linear Approximations in Calculus: Intuition and Examples
http://www.intuitive-calculus.com/linear-approximations.html7c616836e9251ae21a02955a394429a0The linear approximation of functions is one of the most important applications of the derivative. In this page we'll see the intuitive idea behind this and some examples...Wed, 1 Oct 2014 07:51:53 -0400Solving Derivatives: All The Tricks and Techniques
http://www.intuitive-calculus.com/solving-derivatives.htmlbf62959ca8dfc45c9ab9e241cdae35efIn this page you'll find everything you need to know about solving derivatives. My goal with this page is to make you into a derivative solving machine :-)Tue, 23 Sep 2014 09:52:30 -0400The Derivative of The Inverse of a Function: Intuition and Examples
http://www.intuitive-calculus.com/derivative-of-inverse.html9f1f774365b2a6052f1701692e11692fThe rule for the derivative of the inverse of a function has always been a confusing point for students. In this page I explain this topic detail, so you can leave without any doubt about it...Mon, 22 Sep 2014 07:46:47 -0400The Derivative of an Integral: Intuition and Examples
http://www.intuitive-calculus.com/derivative-of-an-integral.htmlb0217683e2d26078d6381db86fea89deWhat is the derivative of an integral? This question is asked by many readers, so I decided to write a special page to explain this topic in detail. It happens that the derivative is the inverse...Mon, 15 Sep 2014 08:20:43 -0400The Derivative of tan(x)
http://www.intuitive-calculus.com/derivative-of-tan.html5cbe073ac02495da5e645b6b27945257The derivative of tan(x) is 1/cos^2(x). We'll prove this fact using a simple method, which involves only the product rule.Sat, 13 Sep 2014 10:27:23 -0400Formulas for the Derivative of Inverse Trig Functions
http://www.intuitive-calculus.com/derivative-of-inverse-trig-functions.html511d695978187714399ef10a8567324cIn this page you'll find the formulas for the derivative of inverse trig functions. These formulas are quite useful and easy to forget. I'll also show you an easy method for deducing these formulas...Fri, 12 Sep 2014 08:25:29 -0400Implicit Differentiation: Intuition and Examples
http://www.intuitive-calculus.com/implicit-differentiation.htmlde64ceca75d2f7f47fd531c1c1d21f94Implicit differentiation confuses many calculus students. That's not because it is hard. In fact, it is just an application of the chain rule. And that's the secret...Thu, 11 Sep 2014 07:54:17 -0400The Derivative of ln(x): Intuition, Proof and Examples
http://www.intuitive-calculus.com/derivative-of-ln.htmldd8f0544170cded13cb36fe2b8d502a6In this page we'll prove the formula for the derivative of ln(x), and we'll also give it some intuitive meaning. Then we'll solve tons of examples involving derivaitves of logarithms...Tue, 9 Sep 2014 10:05:52 -0400Derivative of e^x: Calculating Derivatives of Exponential Functions
http://www.intuitive-calculus.com/derivative-of-e-x.htmlc36133356f99fc7b665d2af87e722aafThe exponential function is one of the most important functions in calculus. In this page we'll deduce the expression for the derivative of e^x and apply it to calculate other problems...Thu, 4 Sep 2014 07:52:44 -0400Calculating the Derivative by Definition
http://www.intuitive-calculus.com/derivative-by-definition.htmlff1ba7d39e40d32663ac353df755dc03In this page we'll learn how to calculate the derivative by definition. This simply involves solving a limit. We'll also learn some of the basic properties of the derivative.Sun, 24 Aug 2014 10:26:56 -0400Continuous Compound Interest and Number e
http://www.intuitive-calculus.com/continuous-compound-interest.htmld324303ab78d57e22cc412bba8010959In this page we'll learn about continuous compound interest and the mysterious number e. The law of compound interest is a universal law that applies not only finance...Sun, 17 Aug 2014 10:53:41 -0400Chain Rule: Physical Intuition and Foolproof Derivative-Solving Technique
http://www.intuitive-calculus.com/chain-rule.html00c4f518d1b44a952f7bb1c9a369ae98The chain rule is usually presented as an arbitrary algebraic rule you must memorize. Here we will first explore the physical intuition behind it, and then learn...Fri, 18 Jul 2014 13:04:48 -0400Derivatives of Trigonometric Functions: An Intuitive Graphical Approach
http://www.intuitive-calculus.com/derivatives-of-trigonometric-functions.html3de34b50204b1f3c2f5a43c228aa4df3In this page I'll show you an intuitive graphical method for the deduction of the derivatives of trigonometric functions. This will build your intuition of trigonometric functions...Tue, 15 Jul 2014 12:29:41 -0400The Definition of Derivative: An Intuitive Introduction
http://www.intuitive-calculus.com/definition-of-derivative.html18b6ad538d4edf4eaae136e5387d2713In this page we'll introduce the definition of derivative in calculus. We'll focus on the intuitive notions that naturally lead to this concept.Sun, 13 Jul 2014 11:29:17 -0400Limits and Continuity: An Intuitive Introduction
http://www.intuitive-calculus.com/limits-and-continuity.htmla089d32f69195eddf1d0843a126c93c6In this page we try to intuitively understand the concepts of limits and continuity. The basic ideas presented here form the foundation of a deep understanding of calculus.Thu, 10 Jul 2014 11:31:52 -0400Product Rule: Intuition Behind It and Solved Problems
http://www.intuitive-calculus.com/product-rule.html038694f8b38e039b28de1709c46e4a2bMost teachers and textbooks introduce the product rule with a formal deduction. Instead, in this page we'll focus first on intuitivelly understanding this rule.Wed, 9 Jul 2014 12:01:00 -0400Intuitive Calculus' One-on-One Calulus Tutor
http://www.intuitive-calculus.com/intuitive-calculus-questions.htmlbdc8c951e97d1eabb8514ef70631f9cfHere you can post your questions about anything related to calculus. Other visitors and I will try to answer your questions the best we could, as quickly as possible. A new page will be created on thSat, 28 Jun 2014 12:10:13 -0400Day 21 of the Free Online Calculus Course: The Fundamental Theorem of Calculus
http://www.intuitive-calculus.com/free-course-integrals-day21.html08ee71eb17623badae0094f5e1cce92aWelcome to Day 21. Today we are going to learn about the Fundamental Theorem of Calculus. We are going to focus on the intuitive idea and how to use it to solve problems.Wed, 20 Nov 2013 08:30:37 -0500Day 20 of the Intuitive Online Calculus Course: Definite Integrals
http://www.intuitive-calculus.com/free-course-integrals-day20.htmldd409ca5b3e2ce5fca90a7322824e0cfToday we are going to introduce the concept of definite integral. We start developing the intuitive idea of this concept with a simple physical example.Thu, 14 Nov 2013 06:03:47 -0500Day 19 of the Intuitive Online Calculus Course: Trigonometric Integrals
http://www.intuitive-calculus.com/free-course-integrals-day19.htmlc03793c01d440d00993e9e54e7ccd3e0Today we focus on solving integrals that involve trigonometric functions. We classify them and then solve examples of each case.Tue, 5 Nov 2013 06:33:09 -0500Day 18 of the Intuitive Online Calculus Course: Trigonometric Substitution
http://www.intuitive-calculus.com/free-course-integrals-day18.htmlebccfbe91e3eb4971b945b9920be57ccToday we learn trigonometric substitution. This is another technique for solving integrals. We are going to learn how to solve each case in which this trick can be applied.Tue, 29 Oct 2013 07:01:08 -0400Limits to infinity of fractions with trig functions
http://www.intuitive-calculus.com/limits-to-infinity-of-fractions-with-trig-functions.htmled148e333857a0c6711f25b392f9d22eThe problem is as follows: d(t)= 100 / 8+4sin(t) Find the limit as t goes to infinity. It is assumed that t>0. How would this work? I know that lim t->infFri, 25 Oct 2013 07:08:19 -0400Day 17 of the Intuitive Online Calculus Course: Integration by Parts
http://www.intuitive-calculus.com/free-course-integrals-day17.html093bbaac43e022c44b2ad99ae58a3a13On Day 17 we learn about integration by parts. This is a very important technique of integration that is like the product rule in reverse.Thu, 24 Oct 2013 09:08:24 -0400Day 16 of the Intuitive Online Calculus Course: Integration by Substitution
http://www.intuitive-calculus.com/free-course-integrals-day16.htmle2ecdad3e9648494b58ef2367fc56f54Welcome to Day 16! Today we are going to learn the first technique for solving integrals: substitution. We'll see that what really is behind this technique is the chain rule.Wed, 23 Oct 2013 10:31:22 -0400Day 15 of the Intuitive Online Calculus Course: Indefinite Integrals
http://www.intuitive-calculus.com/free-course-integrals-day15.html5dc47a24313b4f4da311d7065034631dToday we are going to begin our study of integrals. We present the concept of indefinite integral and solve some examples.Thu, 17 Oct 2013 08:37:40 -0400What are your Biggest Frustrations or Problems with Calculus?
http://www.intuitive-calculus.com/survey.html8acea3d99c770665f1e4ea9c4c2204b9Let me know about them by completing this survey. This information is important to me, so, as a reward for participating, you'll receive a nice surprise gift after you submit your answers!Tue, 24 Sep 2013 10:14:25 -0400Day 14 of the Intuitive Online Calculus Course: Implicit Differentiation
http://www.intuitive-calculus.com/free-course-derivatives-day14.html707c4a2064c3c315d8a476c2691c52adToday we are going to learn about implicit differentiation, a technique that allows us to find derivatives of implicit functions.Mon, 16 Sep 2013 11:59:55 -0400Day 13 of the Intuitive Online Calculus Course: Product Rule and Quotient Rule
http://www.intuitive-calculus.com/free-course-derivatives-day13.html7265dbb2783d4592dd258b680c00a27eThis is Day 13 of the Intuitive Online Calculus Course. Today we are going to learn how to find derivatives of products and quotients of functions.Thu, 12 Sep 2013 12:53:37 -0400Day 12 of the Intuitive Online Calculus Course: The Chain Rule
http://www.intuitive-calculus.com/free-course-derivatives-day12.html46a46d696ac42fe426849e7d91098b49This is Day 12 of the Intuitive Online Calculus Course. Today we are going to learn about the chain rule. This rule allows us to calculate derivatives of more interesting functions.Tue, 3 Sep 2013 20:16:01 -0400The Free Online Calculus Course by Intuitive Calculus
http://www.intuitive-calculus.com/online-calculus-course.html40ed0ebbbb91e1642bb20a4d59ef7384Most online calculus courses are not complete or are too easy. In this course, you'll learn everything you need to know in calculus, even the most difficult concepts, step by step. Tue, 3 Sep 2013 20:14:40 -0400Day 11 of the Intuitive Online Calculus Course: Trigonometric Derivatives
http://www.intuitive-calculus.com/free-course-derivatives-day11.html83523e74ace557736836b60b3c92ba9eOn Day 11 of the Intuitive Online Calculus Course we are going to find derivatives of trigonometric functions. We begin with the basic functions sin(x) and cos(x).Thu, 29 Aug 2013 09:52:49 -0400Day 10 of the Intuitive Online Calculus Course: Derivatives by Definition
http://www.intuitive-calculus.com/free-course-derivatives-day10.html6ebf6d7d6e5b1a286b3b3e529d065ae8This is Day 10 of the Intuitive Online Calculus Course. Today we are going to use the definition of the derivative to actually find some derivatives.Mon, 26 Aug 2013 10:02:06 -0400Day 9 of Online Calculus Course: Physical Interpretation of the Derivative
http://www.intuitive-calculus.com/free-course-derivatives-day9.html3eaed32a54ed0922261c6b742a1aab28This is Day 9 of the Free Online Calculus Course. Today we are going to learn how we can think about the derivative as a physical concept.Wed, 21 Aug 2013 15:25:21 -0400Day 8 of Intuitive Online Calculus Course: Geometric Meaning of the Derivative
http://www.intuitive-calculus.com/free-course-derivatives-day8.htmlc17c12ff19b93af62349a695f08ba676In Day 8 we are going to present the derivative as a geometric concept. We are going to explore this idea to get to a definition.Mon, 19 Aug 2013 09:40:03 -0400Day 7 of the Intuitive Online Calculus Course: Limits at Infinity
http://www.intuitive-calculus.com/free-course-limits-day7.htmlda4861a2f508940841ffd7bfd9dcb653In Day 7 of the Intuitive Online Calculus Course we focus on limits at infinity, that is, limits where x approaches infinity.Fri, 16 Aug 2013 08:35:58 -0400Day 6 of the Intuitive Online Calculus Course: Trigonometric Limits
http://www.intuitive-calculus.com/free-course-limits-day6.html538093013249975e5ac28383ea7687adWelcome to Day 6 of the Intuitive Online Calculus Course. Today we're going to learn how to solve trigonometric limits.Thu, 15 Aug 2013 09:59:14 -0400Day 5 of the Intuitive Online Calculus Course: The Squeeze Theorem
http://www.intuitive-calculus.com/free-course-limits-day5.htmlb3a940518bddb9f9bc0311f991a9c69fWelcome to Day 5 of the Intuitive Online Calculus Course. Today we are going to learn about an important theorem: The Squeeze Theorem. Wed, 14 Aug 2013 10:01:23 -0400Day 4 of the Free Limits eCourse: Limits by Rationalization
http://www.intuitive-calculus.com/free-course-limits-day4.htmldd38075d94efe4401c57cec3b278676aWelcome to Day 4 of the Intuitive Online Calculus Course. Today we're going to learn another algebraic technique for solving limits: rationalization.Tue, 13 Aug 2013 09:43:26 -0400Day 3 of the Free Limits eCourse: Limits by Factoring
http://www.intuitive-calculus.com/free-course-limits-day3.html4ecb2beaa270b1c73bcfb384bdac59fdWelcome to day 3 of the free Intuitive Online Calculus Course. Today we're going to learn how to solve limits by factoring.Mon, 12 Aug 2013 09:45:40 -0400Second Video of The Online Calculus Course: Basic Properties of Limits
http://www.intuitive-calculus.com/calculus-blog.html#Second-Video-of-The-Online-Calculus-Course-Basic-Properties-of-Limitsae3d7331fd335b7311af8260a8ae48c7In this second video we focus on the basic properties of limits and then we solve some simple problems. Check it out!Wed, 7 Aug 2013 14:33:40 -0400Check out First Video of New Online Calculus Course
http://www.intuitive-calculus.com/calculus-blog.html#Check-out-First-Video-of-New-Online-Calculus-Course70d9d1240ad16f987a441b327742a05fThis is the first video ("Day 1") of an upcoming online calculus course that I'm working on. I call each lesson a "day". In this first video we talk about the intuitive idea behind limits, and the notation used for them in calculus. Check it out!Tue, 6 Aug 2013 09:36:02 -0400Calculus Videos
http://www.intuitive-calculus.com/calculus-videos.html8d6b723ce20e81cbea6699872527edbfLearn by watching these calculus videos: get the intuition and solve any problem!Mon, 13 May 2013 10:09:21 -0400Check out the facebook page and new videos!
http://www.intuitive-calculus.com/calculus-blog.html#Check-out-the-facebook-page-and-new-videosed206f3546e08ed9d62ee47c710aee41Check the new facebook page. I posted the new videos on the site. Check them out and leave us a comment...Wed, 8 May 2013 09:39:31 -0400Combination of Product Rule and Chain Rule Problems
http://www.intuitive-calculus.com/combination-of-product-rule-and-chain-rule-problems.htmlf395dae54aa61fbc63e2099cb599c839How do we find the derivative of the following functions? Answer by Pablo: In these two problems posted by Beth, we need to apply not only the chainMon, 19 Nov 2012 07:17:17 -0500Finding the Domain of Composite Functions With Square Roots
http://www.intuitive-calculus.com/finding-the-domain-of-composite-functions-with-square-roots.html20f138bd7d88757171eb3ab7450c7ed6Given the following functions: How do I find the domain of the composite functions fog and gof? Answer by Pablo: Whenever we have functions withMon, 12 Nov 2012 07:18:47 -0500Example of Function That Can Be Differentiated Only Once
http://www.intuitive-calculus.com/example-of-function-that-can-be-differentiated-only-once.htmldb051397e63e31d3860f142bdf1fe42bCan you give me an example of a function that can be differentiated only once? Answer by Pablo: The first example that comes to mind is: The derivativeSat, 27 Oct 2012 09:00:25 -0400