MATH 150 - CORRECTIONS
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(MINOR) CORRECTIONS FOR FALL 2011
2.3.16 (bottom): Replace Òdominant
term in D(x)Ó (which does work, though) with Òhighest power of x in D(x).Ó
2.8.21: Footnote 7 title: É discontinuous at every
rational point.
THE FOLLOWING CORRECTIONS WERE MADE ONLINE AT
ABOUT 2:35am ON 8/21/11.
THE BOOKSTORE COPIES DO NOT HAVE THESE
CORRECTIONS.
2.1.3: An asymptote is a line that a graph
approaches in a long-run or explosive sense. We will discuss this later in 2.3
and 2.4.
2.1.12: Replace f(3) with g(3).
2.1.18: In Section 2.1, there are two ÒExample
11Ós. Renumber the examples.
2.2.2: In Property #6, the word ÒpowerÓ should be
replaced with Òroot.Ó
2.2.3: Replace f(4) with h(4).
SECTION 2.3: BE
CAREFUL WHEN USING DTS! ITÕS BEST FOR ÒEASYÓ PROBLEMS!
CORRECTION FOR 2.3:
Warning
about DTS (2.3)
Delete Page 2.3.26 in
bookstore copies. We shouldnÕt factor
pieces of the numerator and the denominator and eliminate Òlocal factorsÓ as we
take limits, because they could have a real impact on the overall limit.
2.3.11: Add: Think of
(inf)^(-inf) as 1/(inf^inf)
2.3.14: Update Why
does this work? The Factoring Principle of Dominance:
If the dominant term is factored out of an expression,
we obtain the dominant term times something approaching 1.
The Òlong-runÓ limit of the expression is therefore the limit of the
dominant term, and the factor approaching 1 can be removed when figuring out
the ÒfinalÓ limit. This procedure can be applied to the numerator and the
denominator of a fraction separately.
2.3.25 (top box): Add: provided there is no problem
with expressions being defined, and there are no ÒtiesÓ as in the online
example.
2.5.2: Limit Form 1/0 could be DNE.
2.5.5 (top): Limit Form is (-1)/0, not 0/0.
2.5.6 (box): We get a VA at x=a if there are (x-a)
factors in the denominator that cannot be canceled out. We get a hole if we
start with a 0/0 form, but all (x-a) factors in the denominator are canceled
out by the ones in the numerator.
2.6.9 (middle): Replace x^2 with x.
2.8.15 (IVT: Informal Statement): Replace Òevery
function valueÓ with Òevery real value.Ó
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CORRECTIONS FOR SPRING 2010 (VERSION 1.1) CORRECTED
BY 2/5/10
¥ On the old quiz solutions, #1, the first sentence
of the solution should have ÒoddÓ and not Òeven.Ó (Corrected
2/5/10)
¥ In the answer to 2.3, #5, replace (sin x) / (sin
x), which is undefined at x = pi*n (n integer) and has no long-run limits, with
(sin x + 2) / (sin x + 2), whose long-run limits are both 1. (Corrected 2/5/10)
CORRECTIONS FOR FALL 2009 (VERSION 1.0)
CORRECTED BY 12/14/09
2.1.3: An asymptote is a line that a graph approaches
in a long-run or explosive sense. We will discuss this later in 2.3 and 2.4.
2.1.11: Switch the titles ÒLeft-Hand LimitÓ and
ÒRight-Hand Limit.Ó
2.2.5 (in box): no radicand of an even root É
HW for Ch.3:
On 3.2, #6b, there is a
cusp at the origin; ignore the Òfollow upÓ comment. The classic case where you
have a vertical tangent line at the origin, but you donÕt have a corner or a
cusp there, is given by f(x) = x^(1/3). (Can
you see why thereÕs neither a corner nor a cusp?)
On 3.8, #6, the answer
was corrected.
HW for Ch.7 (corrected by
12/11/09): In the answer to 7.5, #1c, there should be an Òln 10Ó factor
in the denominator.
HW for Ch.8 (corrected by
12/14/09): In the answer to 8.3, #4f, there should be a ÒsquareÓ on the
Òcsch.Ó
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