How to Symbolab Inequalities

Solving inequalities is very much like solving equations, but when solving equations you try to find points, when solving inequalities you try to find intervals.

Let’s start with an example of a linear inequality:

If you remember the inequalities properties, mainly that multiplication or division by a negative number reverses the inequality, you should be fine.

Another example, absolute value inequality:

Absolute value, one more thing to pay attention to…

How to solve quadratic inequalities?  First you bring the inequality to the standard form. You can factor it or use the quadratic formula, just like with quadratic equations, but then what? Finding the ranges is somewhat tricky, but once you get the hang of it, it is straightforward.

Let’s try to solve quadratic inequality:

Before you take a look at the steps, you can check the plot, that should give you an idea of where the graph satisfies the inequality, or what might be the range.

Now let’s take a look at the steps:

The table makes it more manageable, that wasn’t too bad, wasn’t it?

Until the next post,
Michal

Symbolab Solutions, Your New Best Friend

You must have noticed that we are constantly adding step-by-step solution to help you with algebra and calculus (If not, make sure to follow us on Twitter @symbolab and Facebook)

So what’s new?  To make step-by-step solutions easy to access, we’ve created a new page, Symbolab Solutions, http://symbolab.com/solutions  How simple?  As easy as it gets.  We’ve added a menu with a list of the topics, a compact pad with friendly must have symbols (if you’re math savvy, you might want to switch to the full pad), and examples per subject.

Simply select a topic from the menu, type in an equation using the pad or click on one of the examples… and Go.   You will get a step-by-step solution and a relevant plot just like that! 

For example (click here):

What else is new?  You can get Step-by-step solutions for System of linear equations, Factor quadratics, Expand, and Definite integrals.  Not only that, but also new and improved plots with an emphasis on the problem.

Check out this integral plot (click here):

Can your best friend do your math homework for you?  Didn’t think so, Symbolab Solutions can, just saying…

Cheers,

Michal

Symbolab and the Future of Search

There is some buzz about the future of search, mainly has to do with Google Knowledge Graph and Star Trek computer (super geeky, I know). 

What does it mean?  The Knowledge Graph is all about intent, attempting to return results based on the meaning of what you search for instead of just literal keyword matches.

It is an important transition from strings to things, from examining keywords to meaning, in other words semantic search; search that takes it beyond mere words and into the world of entities, attributes and the relationship between those entities, such as people, places, sites, sports teams, movies, and more.

For example if you search for Lebron James, Google knows it is a person, not just any person, an NBA player, and gives you back images, a bio, date of birth, height, salary (wow), partner, etc. and related searches that naturally revel top NBA players.  So now the term “Lebron James” refers to an entity rather than keywords.

Now if you think of equations as things, what follow is a scientific knowledge graph of equations, theorems, research topics and more and the connections between these objects.  But is it really a separate graph?  No, there should be no silos; after all it is connected by people, places, by things. 

Why is this so important?  To be able to ask any question (even questions we don’t know how to ask) and get answers, to learn new facts, make predictions, new discoveries.  This is the true sense of science unleashed.

Symbolab is building for the future!

Cheers,

Michal

Integrate This! or how to symbolab integrals

Integrals and derivatives are foundational tools of calculus, with numerous applications in science.  While differentiation has relatively easy rules by which the derivative of a complicated function can be found by differentiating its simpler component functions, integration does not.  Some integration problems require techniques such as substitution, integration by parts, trigonometric identities, trigonometric substitutions, or possibly more than one method.  Integration requires a strategy.

The good news is that Symbolab does that for you now.  We’ve implement smart step-by-step integration solutions.

Best to start with an integration example (click here):

Show steps...

Adding +1-1 to get to a pattern we know how to integrate; now that’s a pretty cool trick!

Let’s try another one (click here):

Show steps...

Substitution, Integration by parts, good strategy…

One more (click here):

And the steps…

Partial fractions decomposition requires practice, but once you get the hang of it the integral becomes relatively simple.

So go practice, do your integrals and don’t forget to let us know if you find this feature helpful.

Integrate this!  Until the next post,
Michal

How to Symbolab Derivatives

Differentiation is fundamental to calculus; it has applications to nearly all quantitative disciplines. For example, in physics, the derivative of the displacement of a moving body with respect to time is the velocity of the body, and the derivative of velocity with respect to time is acceleration.

You probably want to know how to differentiate. Basically, there is a list of rules and known function derivatives (namely trigonometric, hyperbolic, exponential and logarithmic) to apply, but what rule should be used, when and how.  This can be tricky and might require multiple applications of the same rule. Symbolab can help you master derivatives with detailed step-by-step solutions.

How does it work?  Same as before, you type in an equation to differentiate using the pad or text, press the search button to get relevant documentation, solution and plot.

So what’s new?  If you press the show steps you will get detailed description of the solution step-by-step.  Awesome!

Let’s compute a couple of derivatives:

Differentiating exponential and logarithm functions using the chain rule (click here):

Show steps...

Differentiating trigonometric functions using the product and chain rules (click here):

And the steps…

Differentiating hyperbolic functions using the quotient and chain rules (click here):

Steps…

Stay tuned for more step-by-step solutions…

Until the next post,

Michal

How to Symbolab free form equations

Typing equations can be challenging, to make it simple we’ve created the pad.  But most web search engines and tools support text equations (or Latex at best).  If you are used to text equations not to worry, we now support freeform equations (I.e. text and symbols).  Why?  So you can symbolab your way.

How is this different than the generic search engines?  Symbolab understands equations, not just as a collection of keywords and symbols, but the mathematical meaning of the expression.  Symbolab returns solution with steps, plot, and relevant search results, where other search engines just can’t.

Let’s start by solving a quadratic equation - click here

Once you click Enter or Search you will notice the equation transformed into mathematical expression, magic…

Let’s step up to, my favorite, integrals - click here

Search, and...

Ready to mix and match? - try this

Search

Use the pad, type in text or mix and match, do math your way… and make sure you send us feedback.

Until next week,
Michal

Facebook Graph Search – The Future of Search

Facebook Graph Search can’t go unnoted; it is a game changer.

What’s new?  Graph search unlike web search (which is based on keyword search), is trying to understand how people, places and things relate to one another rather than match words to any text. In other words, we can search for people, places, pictures or interests that are on Facebook (...what’s not on Facebook) with specific criteria (intersect people, places and things).  For example: “friends who have been to Paris”, “people who like things I like”, “Indian restaurants in New York liked by friends from India”.  Super cool, right?

Why is it so powerful? because Facebook transforms into a discovery engine.  With over 1 billion users that’s a lot of information right there, we can actually make use of all this data, it is mind blowing.  Think of all the possibilities, look up restaurants by locals or chefs recommendations, fun places to visit by friends or family, movies by experts, meet new people by interest, workplace, location, etc. (huge for professional networking and dating).

What are the problems?  I hear a lot “Like is not really used as a recommendation”, true, but now we know it is; like is the new recommendation, soon enough we’ll adapt, at the end of the day we want to make sure our recommendations count. That said recommendations can be tricky;   we still read the reviews before choosing a hotel, restaurant or a dentist. (cheap is not always good), we need the context, not just the number of likes.  We do trust our friends, just not necessarily their taste in food or music… plus we don’t share so much negative reviews on Facebook (we don’t share enough of anything).  The burning problem is privacy; it is still a big concern (managing what we share with whom, really?)

Privacy aside, we want to make sure our profile has all the information needed to be found in the largest people directory ever.  (Is Linked-in a thing of the past?)

One more thing, make sure you Like Symbolab on Facebook, it is the best equation search engine after all :)

Best,
Michal