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Look, if you had one shot, or one opportunity, To take calculus all over again after a long
year, Would you let it go or do it over again?
No! Your palms are sweaty, unsure and not ready,
First day of calculus starting to learn about limits,
We're nervous, but in the class room look to our calculator for help,
But we realize it's not that hard at all, Here's the point of limits,
Limits can describe how a function behaves, When variables move towards a value,
There's two ways to discover limits, There is graphically and then there is analytically,
Just blew your mind once again, Oh yeah and there's numerically too,
But it sucks, We won't have it, 'cause there's easier ways
than it, It isn't important,
So don't try to do it, And we'll show you why not,
Mainly just because the other two are better, Are you all ready for this?
It will blow your minds, 'cause Nash Dash and Bento are back again
to show you what's up! We gonna teach you guys how to do the limits
yo, You will master it and never let it go,
You get as many tries as you need to get the flow,
This opportunity to learn from us comes once bro,
We gonna teach you guys how to do the limits yo,
You will master it and never let it go, You get as many tries as you need to get the
flow, This opportunity to learn from us comes once
bro, Yeah sucka
First thing's first, graphically comes in ready to burst,
The numbers are ours for solving, The first example problem is ready to be shown,
Say we have x cubed minus one over x minus one for starters,
For all the values of x as it nears one, First you plug the problem into the calculator,
And find when x approaches one from the right, Which in this case should be three,
And now do the same thing for the left side, If done correctly it should be three again,
These are called the left and right-hand limits man,
After these are found there is no more solvin', Though there's a way you must finish it,
And that's to write the limit, In the form the limit from x to one,
X cubed minus one over x minus one is three, And that's all you need to know,
We gonna teach you guys how to do the limits yo,
You will master it and never let it go, You get as many tries as you need to get the
flow, This opportunity to learn from us comes once
bro, We gonna teach you guys how to do the limits
yo, You will master it and never let it go,
You get as many tries as you need to get the flow,
This opportunity to learn from us comes once bro,
Yeah sucka Now here comes the more elaborate one,
This is how we solve limits analytically, Let's take an example of direct substitution,
And we'll show you how to find the solution, Let's use the problem the limit as x goes
to 2, Put that with x squared minus 3x,
Then now plug the limit of 2 into x, So now you get 2 squared minus 3 squared,
If you did it right the answer should be negative 2 kids,
That's the easiest form to use for this, However there are other techniques you can
use to solve these, These problems are easy, make sure you pay
attention please, So when it gets much harder use these tips,
We are going to reveal to you what is known as the three special limits,
All three have the limit from x to 0, First is sinx over x,
If you see it anywhere it will always be 1, Next is 1 minus cosx over x,
Similar to the first if seen anywhere it will be 0,
And last is 1 plus x to the 1 over x exponent, If this problem is seen remember it's e,
Now you have learned those special limits, Practicing is allowed,
Because you only get one shot to learn from the best so go make us proud,
We gonna teach you guys how to do the limits yo, You will master it and never let it go, You get as many tries as you need to get the flow, This opportunity to learn from us comes once bro,