Limits
What is a limit?
The value a function approaches
Define continuity
No breaks, holes, or jumps
Hole means?
Removable discontinuity
What does IVT guarantee?
All values between
Limit of x^2 at 3
9
Evaluate lim x→2 x^2
4
3 conditions?
Defined, limit exists, equals value
Vertical asymptote?
Infinite discontinuity
Condition for IVT
Continuity
Continuous graph drawn how
Without lifting pencil
Evaluate lim x→1 (x^2-1)/(x-1)
2
Is 1/x continuous at 0?
No
Above axis area sign
Positive
f(1)=2, f(3)=6 → value 4?
Yes
sin x derivative?
cos x
lim x→0 sin x / x
1
Type with hole
Removable
Below axis sign
Negative
Why must it pass values?
Continuous
Derivative meaning
Rate of change
When does a limit not exist?
When left ≠ right
Jump occurs when
Left ≠ right
Graph smooth means
Continuous
IVT used to prove
Existence
Integral meaning
Accumulation