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MATH140 Final Cheat Sheet by

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)

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