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Formulas and tips for Calculus1
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 |
Derivative of an Integral
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Limit Definition of Derivatives
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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. |
Rolle's Theorem
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IF: |
- [a,b] is continuous |
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- (a,b) is differentiable |
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- f(a)=f(b) |
THEN: |
f'(c)=0 |
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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