I believe it’s 11n -4 -40
i'm guessing this is asking what percentage it went up by? if so it went up by 190.47 percent. ***400,000 / 210,000 = 1.9047619***
<span>The
content of any course depends on where you take it--- even two courses
with the title "real analysis" at different schools can cover different
material (or the same material, but at different levels of depth).
But yeah, generally speaking, "real analysis" and "advanced calculus"
are synonyms. Schools never offer courses with *both* names, and
whichever one they do offer, it is probably a class that covers the
subject matter of calculus, but in a way that emphasizes the logical
structure of the material (in particular, precise definitions and
proofs) over just doing calculation.
My impression is that "advanced calculus" is an "older" name for this
topic, and that "real analysis" is a somewhat "newer" name for the same
topic. At least, most textbooks currently written in this area seem to
have titles with "real analysis" in them, and titles including the
phrase "advanced calculus" are less common. (There are a number of
popular books with "advanced calculus" in the title, but all of the ones
I've seen or used are reprints/updates of books originally written
decades ago.)
There have been similar shifts in other course names. What is mostly
called "complex analysis" now in course titles and textbooks, used to be
called "function theory" (sometimes "analytic function theory" or
"complex function theory"), or "complex variables". You still see some
courses and textbooks with "variables" in the title, but like "advanced
calculus", it seems to be on the way out, and not on the way in. The
trend seems to be toward "complex analysis." hope it helps
</span>
Answer:
Step-by-step explanation:
x
2
+
x
−
6
=
(
x
+
3
)
(
x
−
2
)
x
2
−
3
x
−
4
=
(
x
−
4
)
(
x
+
1
)
Each of the linear factors occurs precisely once, so the sign of the given rational expression will change at each of the points where one of the linear factors is zero. That is at:
x
=
−
3
,
−
1
,
2
,
4
Note that when
x
is large, the
x
2
terms will dominate the values of the numerator and denominator, making both positive.
Hence the sign of the value of the rational expression in each of the intervals
(
−
∞
,
−
3
)
,
(
−
3
,
−
1
)
,
(
−
1
,
2
)
,
(
2
,
4
)
and
(
4
,
∞
)
follows the pattern
+
−
+
−
+
. Hence the intervals
(
−
3
,
−
1
)
and
(
2
,
4
)
are both part of the solution set.
When
x
=
−
1
or
x
=
4
, the denominator is zero so the rational expression is undefined. Since the numerator is non-zero at those values, the function will have vertical asymptotes at those points (and not satisfy the inequality).
When
x
=
−
3
or
x
=
2
, the numerator is zero and the denominator is non-zero. So the function will be zero and satisfy the inequality at those points.
Hence the solution is:
x
∈
[
−
3
,
−
1
)
∪
[
2
,
4
)
graph{(x^2+x-6)/(x^2-3x-4) [-10, 10, -5, 5]}
