Section 1
Preview this deck
Intermediate Value Theorem
Front
| 5 | 0 | ||
| 4 | 0 | ||
| 3 | 0 | ||
| 2 | 0 | ||
| 1 | 0 |
Active users
0
All-time users
0
Favorites
0
Last updated
6 years ago
Date created
Mar 1, 2020
Cards (57)
Section 1
(50 cards)
Intermediate Value Theorem
If f is continuous on [a,b] and k is a number between f(a) and f(b), then there exists at least one number c such that f(c)=k
Average Velocity
(Change in Position)/(Change in Time)
Alternative Definition of a Derivative
f '(x) is the limit of the following difference quotient as x approaches c
f'(x)-g'(x)
−√2/2
cos(5π/4)
-csc²(x)
d/dx[cotx]=
-csc²x
f'(g(x))g'(x)
d/dt[v(t)]=
a(t)
-1
cos(π)
Absolute value function
D: (-∞,+∞) R: [0,+∞)
d/dx[cscx]=
-cscxcotx
Square root function
D: (0,+∞) R: (0,+∞)
−1/2
cos(4π/3)
0
cos(3π/2)
Reciprocal function
D: (-∞,+∞) x can't be zero R: (-∞,+∞) y can't be zero
Sine function
D: (-∞,+∞) R: [-1,1]
d/dx[secx]=
secxtanx
When is an object moving right?
v(t) > 0
nx^(n-1)
sec(x)tan(x)
Natural log function
D: (0,+∞) R: (-∞,+∞)
What does the graph y = sin(x) look like?
√3/2
cos(π/6)
Exponential function
D: (-∞,+∞) R: (0,+∞)
Global Definition of a Derivative
When is a object stopped?
v(t) = 0
What does the graph y = tan(x) look like?
f'(x)+g'(x)
Trig Identity: 1=
cos²x+sin²x
Mean Value Theorem
The instantaneous rate of change will equal the mean rate of change somewhere in the interval. Or, the tangent line will be parallel to the secant line.
-sin(x)
1/2
cos(π/3)
f is continuous at x=c if...
d/dx[uv]=
vu'+uv'
Cosine function
D: (-∞,+∞) R: [-1,1]
cf'(x)
sec²(x)
1
Average Acceleration
(Change in Velocity)/(Change in Time)
d/dt[s(t)]=
v(t)
√2/2
cos(π/4)
What does the graph y = cos(x) look like?
When is an object moving left?
v(t) < 0
Extreme Value Theorem
If f is continuous on [a,b] then f has an absolute maximum and an absolute minimum on [a,b]. The global extrema occur at critical points in the interval or at endpoints of the interval.
Horizontal Asymptote
d/dx[u/v]=
(vu'-uv')/v^2
d/dx[tanx]=
sec²x
cos(x)
−√3/2
cos(7π/6)
Section 2
(7 cards)