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