Calculus For Dummies, 2nd Edition (2014)

Part VI. The Part of Tens

IN THIS PART …

Ten simple things you absolutely must know

Ten common mistakes you positively must avoid

Ten things to try as a last resort

Chapter 20. Ten Things to Remember

This chapter contains ten things you should definitely remember. That’s not too much to ask, is it? If your mind is already crammed to capacity, you can make some room by first reading Chapter 21, “Ten Things to Forget.”

Your Sunglasses

If you’re going to have to study calculus, you might as well look good.

If you wear sunglasses and a pocket protector, it’ll ruin the effect.

This factor pattern is quasi-ubiquitous and somewhat omnipresent; it’s used in a plethora of problems and forgetting it will cause a myriad of mistakes. In short, it’s huge. Don’t forget it.

, but Is Undefined

, and so 4 times 2 is 8. If had an answer, that answer times zero would have to equal 5. But that’s impossible, making undefined.

The only exception is , which is undefined. The rule holds for everything else, including negatives and fractions. This may seem a bit weird, but it’s true.

SohCahToa

No, this isn’t a famous Indian chief, just a mnemonic for remembering your three basic trig functions:

Trig Values for 30, 45, and 60 Degrees

This identity holds true for any angle. Divide both sides of this equation by to get ; divide by to get .

The Product Rule

. Piece o’ cake.

The Quotient Rule

: In contrast to the product rule, many students forget the quotient rule. But you won’t if you just remember to begin the answer with the derivative of the top of your fraction, u. This is easy to remember because it’s the most natural way to begin. The rest falls into place.

Where You Put Your Keys

No one can predict what score you’ll get on your next calculus exam — unless, that is, you don’t show up.