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Math Problems
Calculus
Find values of derivatives using limits
If
x
+
6
x+6
x
+
6
is a factor of the polynomial function
h
h
h
, what is the value of
h
(
−
6
)
h(-6)
h
(
−
6
)
?
\newline
A)
0
0
0
\newline
B)
6
6
6
\newline
C)
−
6
-6
−
6
\newline
D)
36
36
36
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Find the derivative of
f
(
x
)
=
x
f(x) = x
f
(
x
)
=
x
at
x
=
−
12
x = -12
x
=
−
12
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
\newline
____
\newline
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Find the derivative of
g
(
x
)
=
x
g(x) = x
g
(
x
)
=
x
at
x
=
8
x = 8
x
=
8
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
\newline
____
\newline
Get tutor help
Find the derivative of
f
(
x
)
=
x
f(x) = x
f
(
x
)
=
x
at
x
=
12
x = 12
x
=
12
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
\newline
____
\newline
Get tutor help
Find the derivative of
g
(
x
)
=
x
g(x) = x
g
(
x
)
=
x
at
x
=
−
12
x = -12
x
=
−
12
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
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Find the derivative of
g
(
x
)
=
16
g(x) = 16
g
(
x
)
=
16
at
x
=
−
17
x = -17
x
=
−
17
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
\newline
____
\newline
Get tutor help
Find the derivative of
k
(
x
)
=
x
k(x) = x
k
(
x
)
=
x
at
x
=
−
7
x = -7
x
=
−
7
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
\newline
____
\newline
Get tutor help
Find the derivative of
f
(
x
)
=
x
f(x) = x
f
(
x
)
=
x
at
x
=
9
x = 9
x
=
9
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
\newline
____
\newline
Get tutor help
Find the derivative of
k
(
x
)
=
−
2
k(x) = -2
k
(
x
)
=
−
2
at
x
=
17
x = 17
x
=
17
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
\newline
____
\newline
Get tutor help
Find the derivative of
k
(
x
)
=
x
k(x) = x
k
(
x
)
=
x
at
x
=
15
x = 15
x
=
15
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
\newline
____
\newline
Get tutor help
Find the derivative of
g
(
x
)
=
x
g(x) = x
g
(
x
)
=
x
at
x
=
10
x = 10
x
=
10
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
\newline
____
\newline
Get tutor help
Find the derivative of
g
(
x
)
=
x
g(x) = x
g
(
x
)
=
x
at
x
=
−
1
x = -1
x
=
−
1
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
\newline
____
\newline
Get tutor help
Find the derivative of
k
(
x
)
=
13
k(x) = 13
k
(
x
)
=
13
at
x
=
20
x = 20
x
=
20
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
Get tutor help
Find the derivative of
k
(
x
)
=
x
k(x) = x
k
(
x
)
=
x
at
x
=
−
8
x = -8
x
=
−
8
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
\newline
____
\newline
Get tutor help
Find the derivative of
k
(
x
)
=
20
k(x) = 20
k
(
x
)
=
20
at
x
=
17
x = 17
x
=
17
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
\newline
____
\newline
Get tutor help
Find the derivative of
k
(
x
)
=
x
k(x) = x
k
(
x
)
=
x
at
x
=
5
x = 5
x
=
5
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
\newline
____
\newline
Get tutor help
Find the derivative of
k
(
x
)
=
x
k(x) = x
k
(
x
)
=
x
at
x
=
10
x = 10
x
=
10
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
\newline
____
\newline
Get tutor help
Find the derivative of
f
(
x
)
=
x
f(x) = x
f
(
x
)
=
x
at
x
=
8
x = 8
x
=
8
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
\newline
____
\newline
Get tutor help
Find the derivative of
k
(
x
)
=
x
k(x) = x
k
(
x
)
=
x
at
x
=
4
x = 4
x
=
4
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
\newline
____
\newline
Get tutor help
Find the derivative of
k
(
x
)
=
x
k(x) = x
k
(
x
)
=
x
at
x
=
18
x = 18
x
=
18
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
\newline
____
\newline
Get tutor help
Find the derivative of
f
(
x
)
=
x
f(x) = x
f
(
x
)
=
x
at
x
=
1
x = 1
x
=
1
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
\newline
____
\newline
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How are the solutions to the inequality
−
3
x
≥
18
-3x \geq 18
−
3
x
≥
18
different from the solutions to
−
3
x
>
18
-3x > 18
−
3
x
>
18
? Explain your reasoning.
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\begin{aligned} 3x-4y&=10 \newline 2x-4y&=6 \end{aligned}If
x
x
x
satisfies the given system of equations, what is the value of
x
x
x
?
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Solve the system of equations.
\newline
7
y
+
10
x
−
8
=
0
2
y
−
5
x
−
18
=
0
\begin{aligned} &7y+10x - 8=0 \\\\ & 2 y-5x-18=0 \end{aligned}
7
y
+
10
x
−
8
=
0
2
y
−
5
x
−
18
=
0
Get tutor help
gradient of
y
=
4
x
2
−
6
x
−
5
y=4x^2-6x-5
y
=
4
x
2
−
6
x
−
5
at
x
=
1.5
x=1.5
x
=
1.5
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f
(
x
)
=
x
−
1
f(x) = \sqrt{x} - 1
f
(
x
)
=
x
−
1
If the index is even, determine at least
3
3
3
points, including the key point. If the index is odd, determine at least
5
5
5
points.
Get tutor help
−
6.4
x
=
4
y
+
2.1
-6.4x=4y+2.1
−
6.4
x
=
4
y
+
2.1
\newline
k
y
+
3.2
x
=
5.8
ky+3.2x=5.8
k
y
+
3.2
x
=
5.8
Get tutor help
0.7
a
−
0.8
b
=
−
0.1
a
−
1.4
=
−
6
(
b
−
0.1
)
\begin{aligned} 0.7 a - 0.8b &= -0.1\ a - 1.4 &= -6(b - 0.1) \end{aligned}
0.7
a
−
0.8
b
=
−
0.1
a
−
1.4
=
−
6
(
b
−
0.1
)
Get tutor help
Find the derivative of
f
(
x
)
=
3
x
f(x)=3x
f
(
x
)
=
3
x
at
x
=
2
x=2
x
=
2
Get tutor help
Find
P
3
P_{3}
P
3
for
f
(
x
)
=
ln
x
f(x)=\ln x
f
(
x
)
=
ln
x
centered at
c
=
2.
c=2.
c
=
2.
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Solve the equation. Check your solution.
\newline
4
x
−
8
+
2
x
=
−
32
4 x-8+2 x=-32
4
x
−
8
+
2
x
=
−
32
\newline
The solution set is
_
_
_
_
_
\_\_\_\_\_
_____
.
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Find the derivative of
\newline
f
(
x
)
=
3
x
f(x)=3x
f
(
x
)
=
3
x
at
\newline
x
=
2
x=2
x
=
2
Solution:
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What is the value of
d
d
x
(
x
−
3
)
\frac{d}{d x}\left(x^{-3}\right)
d
x
d
(
x
−
3
)
at
x
=
3
x=3
x
=
3
?
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What is the value of
d
d
x
(
1
x
)
\frac{d}{d x}\left(\frac{1}{x}\right)
d
x
d
(
x
1
)
at
x
=
6
x=6
x
=
6
?
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What is the value of
d
d
x
(
x
)
\frac{d}{d x}(\sqrt{x})
d
x
d
(
x
)
at
x
=
9
x=9
x
=
9
?
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