Cheatography

# MATH140 Final Cheat Sheet by 02gguzman

Formulas and tips for Calculus1

### Limits ### One Sided Limits

 Show that the side you are evaluating exists If it is defined @ value plug it in

### First/ Second Derivative Tests

 First Second 1. Take derivative and find c.v. 1. Take and find c.v. 2. Use a sign chart 2. Use a sign chart + is inc. / - is dec. + is CC up / - is CC down shows extrema shows inflection points * test endpoints *if checking extrema sign is the opposite

### Area Between Curves ### Derivative of an Integral ### Limit Definition of Deriva­tives ### Power Rule ### Produc­t/Q­uotient Rule ### Chain Rule ### Interm­ediate Value Theorem

 IF f is a function that is continuous over the interval [a,b] and m is some number between f (a) and f (b), THEN there exists a number c between and b such that f (c)=m.

### Mean Value Theorem ### Rolle's Theorem

 IF: - [a,b] is continuous - (a,b) is differ­ent­iable - f(a)=f(b) THEN: f'(c)=0

### Newton Raphson Method ### Related Rates

 1. Draw a picture and label 2. Use formula for area/v­olume of shape 3. Take derivative of formula 4. Plug in values to each formula as needed *One variable will NOT have a rate of change (ex. ladder)