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Math Problems
Calculus
Determine end behavior of polynomial and rational functions
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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YOUR WORK. Don't forget units! (
2
2
2
pt)
\newline
1
2
a
\frac{1}{2} a
2
1
a
\newline
\qquad
\newline
\qquad
\newline
\qquad
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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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f
(
x
)
=
72
ln
(
x
)
f(x) = 72 \ln(x)
f
(
x
)
=
72
ln
(
x
)
for
x
<
0
x < 0
x
<
0
for
∞
>
0
\infty > 0
∞
>
0
Find
lim
x
→
+
1
f
(
x
)
\lim_{x \to +1} f(x)
lim
x
→
+
1
f
(
x
)
. Choose
1
1
1
answer:
\newline
(A)
0
0
0
\newline
(B)
1
1
1
\newline
(C)
e
e
e
\newline
(D) The limit doesn't exist.
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f
(
x
)
=
72
ln
(
x
)
f(x) = 72 \ln(x)
f
(
x
)
=
72
ln
(
x
)
for
x
<
0
x < 0
x
<
0
for
∞
>
0
\infty > 0
∞
>
0
Find
lim
x
→
+
1
f
(
x
)
\lim_{x \to +1} f(x)
lim
x
→
+
1
f
(
x
)
. Choose
1
1
1
answer:
\newline
(A)
0
0
0
\newline
(B)
1
1
1
\newline
(C)
e
e
e
\newline
(D) The limit doesn't exist
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Let
lim
x
→
2
+
(
g
(
x
)
)
=
5
\lim_{x \to 2^+}(g(x))=5
lim
x
→
2
+
(
g
(
x
))
=
5
,
lim
x
→
2
−
(
g
(
x
)
)
=
−
5
\lim_{x \to 2^-}(g(x))=-5
lim
x
→
2
−
(
g
(
x
))
=
−
5
. find
lim
x
→
2
(
g
(
x
)
)
\lim_{x \to 2}(g(x))
lim
x
→
2
(
g
(
x
))
if it exists
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Let
lim
x
→
1
(
v
(
x
)
)
=
2
\lim_{x \to 1}(v(x))=2
lim
x
→
1
(
v
(
x
))
=
2
. find
lim
x
→
1
+
(
v
(
x
)
)
\lim_{x \to 1+}(v(x))
lim
x
→
1
+
(
v
(
x
))
and
lim
x
→
1
−
(
v
(
x
)
)
\lim_{x \to 1-}(v(x))
lim
x
→
1
−
(
v
(
x
))
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Let
lim
x
→
1
(
v
(
x
)
)
=
\lim_{x \to 1}(v(x))=
lim
x
→
1
(
v
(
x
))
=
. find
lim
x
→
1
+
(
v
(
x
)
)
\lim_{x \to 1^+}(v(x))
lim
x
→
1
+
(
v
(
x
))
and
lim
x
→
1
−
(
v
(
x
)
)
\lim_{x \to 1^-}(v(x))
lim
x
→
1
−
(
v
(
x
))
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IATICS SPRING
2024
2024
2024
GILBERTSEN
\newline
Use the properties of limits to help decide
w
\mathrm{w}
w
\newline
lim
x
→
1
x
2
−
1
x
2
−
3
x
+
2
\lim _{x \rightarrow 1} \frac{x^{2}-1}{x^{2}-3 x+2}
x
→
1
lim
x
2
−
3
x
+
2
x
2
−
1
\newline
A.
−
1
-1
−
1
\newline
B. Does not exist
\newline
C.
0
0
0
\newline
D.
−
2
-2
−
2
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Subtract the following fractions:
\newline
2
1
9
−
7
9
2 \frac{1}{9}-\frac{7}{9}
2
9
1
−
9
7
\newline
Remember to simplify your answer if possit
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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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Bytelearn. \& Spp.
\newline
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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Question Details
\newline
Done
\newline
Simplify each polynomial expression. Us 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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y
+
k
=
y
+
1
\sqrt {y+k}=y+1
y
+
k
=
y
+
1
For what value of the constant
k
k
k
does the given equation have
y
y
y
as the only solution?
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Since
f
f
f
is the derivative of
g
g
g
, the function
g
g
g
will be increasing on the intervals where
f
f
f
is positive:
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Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval. If the interval of convergence is an Interval, enter your answer using interval notation. If the interval of convergence is a finite set, enter your answer using set notation.)
\newline
∑
n
=
0
∞
(
2
n
)
!
(
x
8
)
n
\sum_{n=0}^{\infty}\frac{(2n)!}{\left(\frac{x}{8}\right)^n}
∑
n
=
0
∞
(
8
x
)
n
(
2
n
)!
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Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval. If the interval of convergence is an interval, enter your answer using interval notation. If the interval of convergence is a finite set, enter your answer usina set notation.)
\newline
∑
n
=
0
∞
(
2
n
)
!
(
x
8
)
n
\sum_{n=0}^{\infty}(2 n) !\left(\frac{x}{8}\right)^{n}
n
=
0
∑
∞
(
2
n
)!
(
8
x
)
n
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Let
f
(
x
)
=
x
−
1
−
2
x
−
5
f(x) = \frac{\sqrt{x-1} - 2}{x-5}
f
(
x
)
=
x
−
5
x
−
1
−
2
when
x
≠
5
x \neq 5
x
=
5
.
\newline
f
f
f
is continuous for all
x
>
1
x > 1
x
>
1
.
\newline
Find
f
(
5
)
f(5)
f
(
5
)
.
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Find the solution of the linear inequaility. Express the soluti the solution set.
\newline
−
3
x
+
4
<
10
−
4
x
-3x+4 < 10-4x
−
3
x
+
4
<
10
−
4
x
\newline
The solution set is the empty set.
\newline
Choose the correct graph below.
\newline
A.
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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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3
3
3
. Determine whether the sequence converges or diverges. If it converges, give the limit.
\newline
a.
{
5
n
+
2
3
n
}
\left\{\frac{5 n+2}{3 n}\right\}
{
3
n
5
n
+
2
}
\newline
b.
{
(
−
1
)
n
−
1
(
5
n
+
2
)
3
n
}
\left\{\frac{(-1)^{n-1}(5 n+2)}{3 n}\right\}
{
3
n
(
−
1
)
n
−
1
(
5
n
+
2
)
}
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Graph the logarithm. Make sure to list the domain and to include any vertical asymptotes on the graph.
(
x
)
=
−
log
3
(
x
+
4
)
+
2
(x)=-\log _{3}(x+4)+2
(
x
)
=
−
lo
g
3
(
x
+
4
)
+
2
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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
The solution set is
{
}
\{\}
{
}
. (Type an integer or a simplified fraction
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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
Get tutor help
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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