Continuities and Derivatives Flashcards
1
Q
Only discontinuous if
- There is no _ (asymptote)
- _ (LHL!=RHL)
- lim(x->a) != _
A
Y value, DNE, f(a)
2
Q
Three steps to prove _
- LHL
- RHL
- LHL=RHL
A
Continuous
3
Q
Intermediate Value Theorem
- Plug in [] in f(x) to get ()
- By the intermediate value theorem, since 0 is between (y range) there is a root on the interval [x range]
A
X range, y range
4
Q
Derivatives
- Plug in f’(x) = lim(h->0) [f(x+h) – f(x)] / h into _
- Simplify
- Cancel h
- Plug in _ for h
A
f(x), 0
5
Q
Solve for f’(a)
- Plug in _ in f’(x) for x
- Plug in f’(x) in _
- Simplify
- Cancel h
- Plug in 0 for h
A
a, f(x)
6
Q
Alternate _
- Plug in a into f’(a) = lim(x->a) [f(x) – f(a)] / (x-a)
- Cancel
A
f’(a)
7
Q
Graphing slope of f’(x)
- _
- Plot + and –
- Plot _
- Graph slope
A
Arrows, 0
8
Q
Prove continuous on (-infinity, infinity)
- lim(x->n+) = _
- Solve
A
lim(x->n-)