Section 1
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Trig Identity: 1=
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Cards (56)
Section 1
(50 cards)
Trig Identity: 1=
cos²x+sin²x
d/dx[secx]=
secxtanx
d/dx[uv]=
vu'+uv'
d/dx[tanx]=
sec²x
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
Exponential function
D: (-∞,+∞) R: (0,+∞)
When is an object moving left?
v(t) < 0
nx^(n-1)
f'(x)-g'(x)
Reciprocal function
D: (-∞,+∞) x can't be zero R: (-∞,+∞) y can't be zero
f'(x)+g'(x)
-csc²(x)
Horizontal Asymptote
What does the graph y = cos(x) look like?
d/dt[v(t)]=
a(t)
Cosine function
D: (-∞,+∞) R: [-1,1]
When is an object moving right?
v(t) > 0
sec(x)tan(x)
f is continuous at x=c if...
What does the graph y = tan(x) look like?
-sin(x)
−√3/2
cos(7π/6)
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.
What does the graph y = sin(x) look like?
1/2
cos(π/3)
sec²(x)
Global Definition of a Derivative
d/dt[s(t)]=
v(t)
−√2/2
cos(5π/4)
0
cos(3π/2)
f'(g(x))g'(x)
When is a object stopped?
v(t) = 0
Average Acceleration
(Change in Velocity)/(Change in Time)
-1
cos(π)
Average Velocity
(Change in Position)/(Change in Time)
d/dx[u/v]=
(vu'-uv')/v^2
d/dx[cotx]=
-csc²x
cf'(x)
Sine function
D: (-∞,+∞) R: [-1,1]
√3/2
cos(π/6)
√2/2
cos(π/4)
d/dx[cscx]=
-cscxcotx
Alternative Definition of a Derivative
f '(x) is the limit of the following difference quotient as x approaches c
−1/2
cos(4π/3)
Square root function
D: (0,+∞) R: (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.
cos(x)
Natural log function
D: (0,+∞) R: (-∞,+∞)
1
Absolute value function
D: (-∞,+∞) R: [0,+∞)
Section 2
(6 cards)