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2. Newton's Law of Cooling

3. L'HÃ´pital's Rule
 lim(f(x)/g(x))=lim(f'(x)/g'(x))
 *If indeterminate forms infinity/infinity, 0/0

4. Limit Definition
 lim(f(x))=L
 x>a
 Provided for any epsilon>0 there exists a delta>0 such that whenever xa

5. Vertical asymptotes
Denom=0, numerator doesn't

6. Horizontal asymptotes
Degree of top <= degree of bottom

7. Oblique
Degree of top is one more than bottom

8. Squeeze theorem
If for all x f(x)<=g(x)<=h(x), for x big and positive, if f(x)>L and h(x)>L, g(x)>L

9. To maximize, minimize
Find critical points, endpoints.

10. Related rates
 1. Write an equation that 2+ quantities which vary with time
 2. Differentiate both sides with respect to time (know rules)
 3. The resulting equation relates the rates at which quantities vary
 4. Solve for what is requested

11. Newton's Method
Let f be any function and x0 any estimate to a root of f. For n>=1, the rule x(n+1)=xnf(xn)/f'(xn) produces a sequence of estimates

12. Taylor polynomial of order n at point x0 is:
 T(x)=f(xn)+f'(x0)(xx0)+f''(x0)/2(xx0)^2+...+f(n)(x0)/n!(xx0)^n
 *Accurate around x0, better if more terms

13. Maclaurin polynomials
X0=0

14. Intermediate Value Theorem
The continuous function f on interval [a,b] takes on all range values between f(a) and f(b) at least once for domains between a and b

15. Location Principle
For continuous function on interval [a,b] if f(a)<0 and f(b)>0, then there is at least one real c between a and b such that f(c)=0

16. Extreme Value Theorem
If f is continuous on [a,b] then f assumes both a max and min value for some domain values in [a,b]

17. Mean Value Theorem
If f is continuous on interval [a,b] and f is differentiable on (a,b), then there exists a c between a and b such that f'(c)=(f(b)f(a))/(ba)

18. Rolle's Theorem
If f is continuous on (a,b) and differentiable on (a,b) and f(a)=f(b) then there exists a c between a and b such that f'(c)=0

