AP Calculus BC Running Notes

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Calculus

40 Terms

1
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What is the derivative of sin x ?
cos x
2
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What is the derivative of tan x ?
sec^2 x
3
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What is the derivative of sec x ?
sec x tan x
4
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What is the derivative of cos x ?
- sin x
5
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What is the derivative of cot x ?
- csc^2 x
6
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What is the derivative of csc x ?
- csc x cot x
7
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What is implied domain?
domains with real numbers
8
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Rule: log (ab) is the same as ?
log a + log b
9
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Rule: log (a/b) is the same as ?
log a - log b
10
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Rule: log (a^n) is the same as ?
n log a
11
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What is the inverse of e^x ?
ln (x)
12
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0 in the denominator is what type of limit ?
Vertical Asymptote
13
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What is the conjugate method ?
Multiply numerator and denominator by fraction part that includes a root to rationalize
14
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When the limit x ➔ 0 , (sinx)/(x) = ?
1
15
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When the limit x ➔ 0 , (1-cosx)/(x) = ?
0
16
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When the limit x ➔ 0 , (1-x)^(1/x) = ?
e
17
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What must be true for something to be continuous ?
limit must exist, c must be defined, limit and c must be the same
18
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What is the greatest integer function ?
f(x) = |x|
19
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What is the intermediate value theorem ?
As long as the space is continuous, a point will exist for what you're trying to find
20
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If the powers are the same, what can be understood ?
just use coefficients
21
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In a fraction, if the power is large on the top, where is x going to ?
infinity
22
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In a fraction, if the power is large on the bottom, where is x going to ?
0
23
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Polynomials in piecewise functions are _________.
continuous
24
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Slope shows _______.
velocity
25
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Derivatives show ______.
Slope of the tangent line, slope of the function at a given point
26
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What is the derivative of e^x ?
e^x
27
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The derivative of any constant is ___.
0
28
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If the function is not continuous, it is said to be __________.
non-differentiable
29
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Differentiability implies _________.
continuity
30
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Continuity does NOT imply _________.
differentiabilitity
31
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Max Height is found when velocity = ?
0
32
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The power rule states ?
dy/dx (x^n) = nx^(n-1)
33
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The constant multiple rule states ?
If there is a constant in front of a function, it tags along.
34
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The sum/difference rule states ?
One can take the derivative of each part separately
35
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The product rule states ?
d/dx [(f(x))(g(x))] = f'(x)g(x) + f(x)g'(x)
36
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The quotient rule states ?
low d high - high d low / low squared
37
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cos^2 (x) + sin^2 (x) = ?
1
38
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What is the derivative of b^x when b is a number excpet 1 ?
b^x ln b
39
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What is the derivative of ln x ?
1/x (no negatives)
40
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What is the derivative of ln |x| ?
1/x (allows negatives)