Calculus 2 Cheat Sheet
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16B Veitch
Calculus 2 Study Guide
This study guide is in no way exhaustive. As stated in class, any type of question from class, quizzes,
exams, and homeworks are fair game.
1. Some Algebra Review
(a) Logarithm Properties
y
i. y = log
x is equivalent to x = b
.
b
ii. log
b = 1
b
iii. log
1 = 0, ln 1 = 0
b
r
r
iv. log
(b
) = r, ln(e
) = r
b
r
r
v. log
(x
) = r log
(x), ln(x
) = r ln(x)
b
b
vi. log
(M N ) = log
(M ) + log
(N )
b
b
b
M
vii. log
= log
(M )
log
(N )
b
b
b
N
viii. The domain of log
(u) is u > 0
b
ix. All the rules above hold for ln x. Remember that ln x = log
x
e
x. Change of Base
ln M
log
M
b
log
(M ) =
=
a
ln a
log
a
b
This is useful if you’re asked to find the derivative of y = log
(x + 1)
5
(b) Exponential Properties
1
n
m
n+m
i. a
a
= a
n
v. a
=
n
a
n
m
nm
ii. (a
)
= a
1
n
vi.
= a
n
n
n
iii. (ab)
= a
b
n
a
n
a
1
n m
iv.
= a
=
m/n
m
1/n
1/n
m
vii. a
= (a
)
= (a
)
m
m n
a
a
(c) Properties of Radicals
1/n
i.
a = a
m/n
m
ii.
a
= a
2. Limits
(a) Notation
i. General Limit Notation: lim
f (x) = L
x
a
ii. Left Hand Limit: lim
f (x) = L
x
a
iii. Right Hand Limit: lim
f (x) = L
x
a
iv. If lim
f (x) = lim
f (x) = L then lim
f (x) = L
x
a
x
a
x
a
1
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