Section 1
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√3/2
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Last updated
6 years ago
Date created
Mar 1, 2020
Cards (57)
Section 1
(50 cards)
√3/2
cos(π/6)
What does the graph y = sin(x) look like?
-1
cos(π)
Square root function
D: (0,+∞) R: (0,+∞)
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.
d/dx[cotx]=
-csc²x
Average Velocity
(Change in Position)/(Change in Time)
sec²(x)
f'(x)-g'(x)
f is continuous at x=c if...
f'(g(x))g'(x)
cos(x)
√2/2
cos(π/4)
−√3/2
cos(7π/6)
nx^(n-1)
-csc²(x)
When is a object stopped?
v(t) = 0
f'(x)+g'(x)
Exponential function
D: (-∞,+∞) R: (0,+∞)
When is an object moving right?
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.
sec(x)tan(x)
d/dx[secx]=
secxtanx
1
−√2/2
cos(5π/4)
What does the graph y = tan(x) look like?
Sine function
D: (-∞,+∞) R: [-1,1]
d/dt[v(t)]=
a(t)
Natural log function
D: (0,+∞) R: (-∞,+∞)
Average Acceleration
(Change in Velocity)/(Change in Time)
Reciprocal function
D: (-∞,+∞) x can't be zero R: (-∞,+∞) y can't be zero
cf'(x)
d/dx[uv]=
vu'+uv'
1/2
cos(π/3)
Trig Identity: 1=
cos²x+sin²x
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
What does the graph y = cos(x) look like?
0
cos(3π/2)
d/dt[s(t)]=
v(t)
Cosine function
D: (-∞,+∞) R: [-1,1]
-sin(x)
Global Definition of a Derivative
−1/2
cos(4π/3)
Horizontal Asymptote
d/dx[tanx]=
sec²x
Alternative Definition of a Derivative
f '(x) is the limit of the following difference quotient as x approaches c
d/dx[u/v]=
(vu'-uv')/v^2
d/dx[cscx]=
-cscxcotx
When is an object moving left?
v(t) < 0
Absolute value function
D: (-∞,+∞) R: [0,+∞)
Section 2
(7 cards)