Limits
x | -0.1 | -0.01 | 0 | 0.01 | 0.1
f(x) | 0.99 | 0.999 |2 | 4.03 | 4.3
The limit of f(x) as x approaches 0
Does Not Exist
Derivative of (sin x)
What is (cos x)?
f is a function that is continuous on [a,b] and differentiable on (a,b), then there is a number on the interval [a,b] such that f(b)-f(a) = f'(c)(b-a)
What is Mean Value Theorem?
x | -0.2 | -0.1 | 0 | 0.1 | 0.2
f(x) | 5 | 4 | DNE | 2 | 1
The limit of f(x) as x approaches 0
3
Derivative of (cos x)
What is (-sin x)?
If f is a continuous function on the interval [a,b], then f has both an absolute maximum value, f(c), and an absolute minimum value, f(d), for some numbers c and d on [a,b]
What is the Extreme Value Theorem?
x | 20 | 40 | 60 | 80 | 100
f(x) | 5 | 13 |26 | 13 | 5
The limit of f(x) as x approaches 60
26
Derivative of (tan x)
What is (sec2 x)?
If f is a continuous function on the interval [a,b], and N is any number between f(a) and f(b), then there is a number, c, in (a, b) such that f(c) = N
What is the Intermediate Value Theorem?
x | 0 |2 | 4 | 6 | 8
f(x) | 15| 25 |0 |45 | 55
The limit of f(x) as x approaches 4
35
Derivative of (cot x)
What is (-csc2 x)?
If f is a function that is continuous on [a,b] and differentiable on (a, b) and f(a)=f(b) then there is a number on [a,b] such that f'(c)=0
What is Rolle's Theorem?
x | -2 |-1 | 0 | 1 | 2
f(x) | 20| 50000 |1 |-50000 | -20
The limit of f(x) as x approaches 0
Does not exist
Derivative of (sec x)
What is (sec x tan x)?
∫ab f(x)dx = F(b) - F(a) where F'(x) = f(x)
What is the Fundamental Theorem of Calculus?