Advanced Math Solutions – Limits Calculator, the basics

The limit of a function is a fundamental concept in calculus concerning the behavior of that function near a particular point.  Limits help us approximate functions for any point x even if the function itself does not exist at that point (to infinity and beyond).

We will start with the substitution method (a.k.a the plug-and-chug method).  Plug in the value to which x is approaching (can’t get easier than this).  The limit is simply the function value.  Pay attention, this method works for limits that involve continuous functions only.

The following limit properties can be useful:

If the limits of f(x), g(x) exist, then:

• \lim_{x\to{a}}[f(x)\pm{g(x)}]=\lim_{x\to{a}}{f(x)}\pm\lim_{x\to{a}}{g(x)}
• \lim_{x\to{a}}[f(x)\cdot{g(x)}]=\lim_{x\to{a}}{f(x)}\cdot\lim_{x\to{a}}{g(x)}
• \lim_{x\to{a}}[c\cdot{f(x)}]=c\cdot\lim_{x\to{a}}{f(x)}
• \lim_{x\to{a}}[\frac{f(x)}{g(x)}]=\frac{\lim_{x\to{a}}{f(x)}}{\lim_{x\to{a}}{g(x)}},\:where\:\lim_{x\to{a}}{g(x)}\neq{0}

Lets start with a simple example (click here):

Here’s another example involving product (click here)

One more example involving quotient  (click here):

That was a breeze.  In the next post we will continue with discontinuous functions

Cheers,
Michal

Practice Makes Perfect

Learning math takes practice, lots of practice.  Just like running, it takes practice and dedication.    If you want to be really good at all types of math, you need to practice them all. You can't trust your innate natural talent to do most of the job for you.  There’s no such thing as math genes!

You must have heard this before, so let’s just do it.  Sign into Symbolab interactive practice (free of charge) and start practicing, it’s that simple (currently available for integrals and derivatives).

Practice:

Each subject is broken down into topics.   The topics are ordered by difficulty level (You can select a new topic any time).  Next to the topic we keep track of the number of problems you answered correctly.   We recommend completing at least 5 problems before moving to the next topic.   Start solving one by one.  If you need help click Next Hint (it will show you how many hints are still available).  When ready type in your answer, click Verify.  You should get instant indication if your answer is correct

If your answer is incorrect try again, ask for more hints.  Take your time, it’s meant for you to learn.


The Quiz:

At any time, you can test yourself by taking a quiz.  Simply select Quiz from the menu (there’s a quiz at the end of each level), click Start Quiz and go.  No hints this time, you will get your test summary at the end.

When to start? Now is as good a time as any…

Cheers,
Michal

My Notebook, the Symbolab way

Math notebooks have been around for hundreds of years.  You write down problems, solutions and notes to go back to when doing your homework or studying  for an exam.   If you skipped class, your dog ate your homework, or you are just not typing fast enough, you have a problem.

Einstein’s notebook:

President Lincoln’s math notebook:

Although notebooks did work well for some of the greatest, it’s time for a change!

Symbolab makes it easy, with My Notebook you can save any problem or example, add your private notes, rank and share.  You can access any subject instantly, no need to flip through your notes,  the solution steps are a click away.

At the bottom of the solution steps there’s a Save button,  just like this:

Click the Save button opens a notepad, you can type your notes (you don’t have to), click Save to save the problem to your notebook.

Voila, this is your notebook with your private problems and notes.  You can edit the notes, share with friends, and rank the difficulty level.  Most important you can get the solution steps.  It’s that easy!

Start your practice zone now, Click here to register.

Cheers,
Michal