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Math Problems
Calculus
Determine end behavior of polynomial and rational functions
Unit test Problem Find the limit as
x
x
x
approaches positive infinity.
\newline
lim
x
→
∞
3
x
−
1
x
2
−
6
=
\lim_{{x \to \infty}} \frac{{3x - 1}}{{\sqrt{{x^2 - 6}}}} =
lim
x
→
∞
x
2
−
6
3
x
−
1
=
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Solve for
v
v
v
. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
\newline
−
42
v
+
33
<
8
v
+
91
-42v + 33 < 8v + 91
−
42
v
+
33
<
8
v
+
91
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Add, subtract, multiply, or divide as indicated to simplify each expression. Remember to work within the parentheses first.
\newline
10
−
(
5
−
3
)
10-(5-3)
10
−
(
5
−
3
)
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Add, subtract, multiply, or divide as indicated to simplify each expression. Remember to work within the parentheses first.
\newline
5
+
(
4
+
3
)
5+(4+3)
5
+
(
4
+
3
)
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Use the limit process to find the area of the region.
\newline
y
=
1
4
x
3
,
[
2
,
4
]
y=\frac{1}{4}x^{3},[2,4]
y
=
4
1
x
3
,
[
2
,
4
]
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Find a point on the line and the line's slope.
\newline
y
−
2
=
−
4
(
x
−
4
)
y-2=-4(x-4)
y
−
2
=
−
4
(
x
−
4
)
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∫
0
α
ln
(
cot
(
α
)
+
tan
(
x
)
)
d
x
\int_{0}^{\alpha} \ln(\cot(\alpha) + \tan(x)) \, dx
∫
0
α
ln
(
cot
(
α
)
+
tan
(
x
))
d
x
, where
α
\alpha
α
is in the interval
0
,
π
2
0, \frac{\pi}{2}
0
,
2
π
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write the degree of following polynomials.
(
i
)
2
x
2
+
3
x
y
+
5
y
2
+
2
(i) 2x^2+3xy+5y^2+2
(
i
)
2
x
2
+
3
x
y
+
5
y
2
+
2
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d
y
d
x
=
−
4
y
\frac{dy}{dx} = -4y
d
x
d
y
=
−
4
y
, and
y
=
3
y=3
y
=
3
when
x
=
2
x=2
x
=
2
. Solve the equation.
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Simplify the rational expression. State any restrictions on the variable.
\newline
t
2
+
t
−
6
t
2
−
9
\frac{t^{2}+t-6}{t^{2}-9}
t
2
−
9
t
2
+
t
−
6
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2
x
+
y
=
6
2 x+y=6
2
x
+
y
=
6
find
x
x
x
when
y
y
y
is
6
6
6
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Simplify each polynomial expression. Use any method of choice.
\newline
SHOW ALL WORK.
\newline
(
4
a
3
−
2
b
+
6
)
−
(
3
a
3
+
2
b
−
9
)
\left(4 a^{3}-2 b+6\right)-\left(3 a^{3}+2 b-9\right)
(
4
a
3
−
2
b
+
6
)
−
(
3
a
3
+
2
b
−
9
)
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Use addition to rewrite the subtraction expression below without changing the digits. Do not solve.
\newline
14
−
(
−
13
)
14-(-13)
14
−
(
−
13
)
\newline
Answer:
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Use addition to rewrite the subtraction expression below without changing the digits. Do not solve.
\newline
17
−
(
−
19
)
17-(-19)
17
−
(
−
19
)
\newline
Answer:
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Use addition to rewrite the subtraction expression below without changing the digits. Do not solve.
\newline
4
−
(
−
12
)
4-(-12)
4
−
(
−
12
)
\newline
Answer:
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Use addition to rewrite the subtraction expression below without changing the digits. Do not solve.
\newline
15
−
(
−
15
)
15-(-15)
15
−
(
−
15
)
\newline
Answer:
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Find the zeros of the function. Enter the solutions from least to greatest.
f
(
x
)
=
(
x
−
5
)
(
5
x
+
2
)
f(x)=(x-5)(5x+2)
f
(
x
)
=
(
x
−
5
)
(
5
x
+
2
)
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Find the zeros of the function. Enter the solutions from least to greatest.
h
(
x
)
=
(
−
4
x
−
5
)
(
−
x
+
5
)
h(x)=(-4x -5)(-x +5)
h
(
x
)
=
(
−
4
x
−
5
)
(
−
x
+
5
)
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For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).
\newline
8
3
,
24
,
24
3
,
…
8 \sqrt{3}, \quad 24, \quad 24 \sqrt{3}, \quad \ldots
8
3
,
24
,
24
3
,
…
\newline
3
3
\frac{\sqrt{3}}{3}
3
3
\newline
3
\sqrt{3}
3
\newline
2
3
2 \sqrt{3}
2
3
\newline
2
3
3
\frac{2 \sqrt{3}}{3}
3
2
3
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Solve the equation. Check your solution
\newline
−
5
(
5
n
−
5
)
=
30
-5(5n-5)=30
−
5
(
5
n
−
5
)
=
30
\newline
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Find the slope-intercept form for the line satisfying the conditions.
\newline
slope
−
6
-6
−
6
, passing through
\newline
(
0
,
1
)
(0,1)
(
0
,
1
)
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Click and drag like terms onto each other to simplify fully.
\newline
−
5
x
−
6
+
2
x
−
1
−
3
y
−
1
-5 x-6+2 x-1-3 y-1
−
5
x
−
6
+
2
x
−
1
−
3
y
−
1
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Click and drag like terms onto each other to simplify fully.
\newline
5
y
−
7
y
−
2
+
6
−
6
5 y-7 y-2+6-6
5
y
−
7
y
−
2
+
6
−
6
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Click and drag like terms onto each other to simplify fully.
\newline
−
5
x
+
5
x
−
5
+
4
x
-5 x+5 x-5+4 x
−
5
x
+
5
x
−
5
+
4
x
\newline
You must answer all questions above in order to submit.
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Click and drag like terms onto each other to simplify fully.
\newline
4
y
−
2
+
3
−
4
x
−
x
4 y-2+3-4 x-x
4
y
−
2
+
3
−
4
x
−
x
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Click and drag like terms onto each other to simplify fully.
\newline
1
−
1
+
5
y
−
4
1-1+5 y-4
1
−
1
+
5
y
−
4
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Determine the following limit in simplest form. If the limit is infinite, state that the limit does not exist (DNE).
\newline
lim
x
→
∞
−
3
x
+
x
4
7
+
8
x
2
+
10
x
\lim _{x \rightarrow \infty} \frac{\sqrt{-3 x+x^{4}}}{7+8 x^{2}+10 x}
x
→
∞
lim
7
+
8
x
2
+
10
x
−
3
x
+
x
4
\newline
Answer:
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What is the average value of
x
3
−
9
x
x^{3}-9 x
x
3
−
9
x
on the interval
−
1
≤
x
≤
3
-1 \leq x \leq 3
−
1
≤
x
≤
3
?
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Let
f
(
x
)
=
6
x
3
3
x
+
2
f(x)=\frac{6 x^{3}}{3 x+2}
f
(
x
)
=
3
x
+
2
6
x
3
.
\newline
Find
lim
x
→
∞
f
(
x
)
\lim _{x \rightarrow \infty} f(x)
lim
x
→
∞
f
(
x
)
.
\newline
Choose
1
1
1
answer:
\newline
(A)
2
2
2
\newline
(B)
3
3
3
\newline
(C)
0
0
0
\newline
(D) The limit is unbounded
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