| Limits | Rules and Theorems | Increasing/Decreasing or Overestimate/Underestamate | Derivatives | Integrals |
|---|---|---|---|---|
|
limx→a- f(x)=limx→a+ f(x)=L
When does the limx→a f(x) exist?
|
f(x) is continuous
What is the extreme value theorem?
|
It is increasing
If f'(x)>0, then f(x) is ____
|
-1/√(1-x^2)
The derivative of inverse cosine is
|
sin(x)+C
∫cos(x) dx
|
|
limx→a f(x) + limx→a g(x)
When does the limx→a (f(x)+g(x))?
|
f'(g(x)) x g'(x)
What is chain rule?
(f(g(x)))' |
It is decreasing
If f'(x)<0, then f(x) is ____
|
1/(1+x^2)
The derivative of inverse tangent is
|
-cos(x)+C
∫sin(x) dx
|
|
limx→a f(x) - limx→a g(x)
When does the limx→a (f(x)-g(x))?
|
f'(x)g(x)+f(x)g'(x)
What is product rule?
(f(x)g(x))' |
It is an overestimate
If the function is increasing, then the right sum is an ____
|
-1/ (lxl √(x^2 - 1))
The derivative of inverse cosecant is
|
e^2 + C
∫e^x dx
|
|
((limx→a f(x)) / (limx→a g(x))) if limx→a g(x)≠0
When does the limx→a ((f(x))/(g(x)))?
When does the limx→a ((f(x))/(g(x)))?
|
(f'(x)g(x)-f(x)g'(x)) / (g(x))^2
What is quotient rule?
(f(x)/g(x))'= |
It is an underestimate
If the function is increasing, than the left sum is an ____
|
1/ (lxl √(x^2 - 1))
The derivative of inverse secant is
|
mx+C
∫m dx
|
|
limx→a f(x) x limx→a g(x)
When does the limx→a (f(x)xg(x))?
|
-f(x) is continuous on [a.b]
-a
What is the intermediate value theorem?
|
It is an underestimate
If the function is decreasing, then the right sum is an ____
|
-1/(1+x^2)
The derivative of inverse cotangent is
|
((x^(n+1)) / (n+1)) +C
∫x^n dx
|
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