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Calculus
Find the slope of a tangent line using limits
Find the slope of the line tangent to the graph of
f
(
x
)
=
log
3
(
3
−
5
x
2
x
−
5
)
f(x)=\log _{3}\left(\frac{3-5 x}{2 x-5}\right)
f
(
x
)
=
lo
g
3
(
2
x
−
5
3
−
5
x
)
at
x
=
2
x=2
x
=
2
.
\newline
Enter an exact answer.
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2
x
+
4
y
=
15
2
x
+
4
y
=
13
\begin{aligned}2x+4y &= 15 \newline2x+4y &= 13\end{aligned}
2
x
+
4
y
2
x
+
4
y
=
15
=
13
\newline
Consider the given system of equations. How many solutions does this system have?
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Something
\newline
Google
\newline
Grades
\newline
R.
9
9
9
Reflections: find the coordinates KUX
\newline
Write the coordinates of the vertices after a reflection over the line
y
=
−
1
y=-1
y
=
−
1
.
\newline
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what are the coordinates of the point on the graph of
y
=
e
3
x
y=e^{3x}
y
=
e
3
x
at which the tangent line to the graph at that point also passes through the origin.
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Question
\newline
Find the slope of the line tangent to the graph of
f
(
x
)
=
−
3
x
2
−
3
x
+
2
f(x)=-3 x^{2}-3 x+2
f
(
x
)
=
−
3
x
2
−
3
x
+
2
at
x
=
1
x=1
x
=
1
.
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12
12
12
. The
2
2
2
parallel sides of a trapezoid measure
8
c
m
8 \mathrm{~cm}
8
cm
and
4
c
m
4 \mathrm{~cm}
4
cm
. If the height is
3
3
3
c
m
\mathrm{cm}
cm
, what is the area of the trapezoid?
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x
=
−
1
x=-1
x
=
−
1
\newline
x
=
1
x=1
x
=
1
\newline
f
(
x
)
=
1
f(x)=1
f
(
x
)
=
1
\newline
g
(
x
)
=
−
1
g(x)=-1
g
(
x
)
=
−
1
\newline
Determine whether pair of function
F
F
F
and
g
g
g
are inverses. Explain. your reasonin.
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For the function
f
(
x
)
=
9
x
2
−
8
x
−
7
f(x)=9 x^{2}-8 x-7
f
(
x
)
=
9
x
2
−
8
x
−
7
, find the slope of the tangent line at
x
=
9
x=9
x
=
9
.
\newline
Answer:
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For the function
f
(
x
)
=
x
2
−
4
f(x)=x^{2}-4
f
(
x
)
=
x
2
−
4
, find the slope of the tangent line at
x
=
−
4
x=-4
x
=
−
4
.
\newline
Answer:
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For the function
f
(
x
)
=
6
x
2
+
11
x
+
7
f(x)=6 x^{2}+11 x+7
f
(
x
)
=
6
x
2
+
11
x
+
7
, find the slope of the tangent line at
x
=
8
x=8
x
=
8
.
\newline
Answer:
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For the function
f
(
x
)
=
x
2
−
10
f(x)=x^{2}-10
f
(
x
)
=
x
2
−
10
, find the slope of the tangent line at
x
=
7
x=7
x
=
7
.
\newline
Answer:
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For the function
f
(
x
)
=
x
2
−
11
f(x)=x^{2}-11
f
(
x
)
=
x
2
−
11
, find the slope of the tangent line at
x
=
−
3
x=-3
x
=
−
3
.
\newline
Answer:
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For the function
f
(
x
)
=
−
9
x
−
9
f(x)=-9 x-9
f
(
x
)
=
−
9
x
−
9
, find the slope of the tangent line at
x
=
−
6
x=-6
x
=
−
6
.
\newline
Answer:
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For the function
f
(
x
)
=
x
2
+
5
f(x)=x^{2}+5
f
(
x
)
=
x
2
+
5
, find the slope of the tangent line at
x
=
5
x=5
x
=
5
.
\newline
Answer:
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For the function
f
(
x
)
=
10
x
+
3
f(x)=10 x+3
f
(
x
)
=
10
x
+
3
, find the slope of the tangent line at
x
=
11
x=11
x
=
11
.
\newline
Answer:
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For the function
f
(
x
)
=
12
x
2
−
11
x
+
8
f(x)=12 x^{2}-11 x+8
f
(
x
)
=
12
x
2
−
11
x
+
8
, find the slope of the tangent line at
x
=
−
7
x=-7
x
=
−
7
.
\newline
Answer:
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For the function
f
(
x
)
=
10
x
2
+
7
x
−
6
f(x)=10 x^{2}+7 x-6
f
(
x
)
=
10
x
2
+
7
x
−
6
, find the slope of the tangent line at
x
=
−
4
x=-4
x
=
−
4
.
\newline
Answer:
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For the function
f
(
x
)
=
x
2
−
3
f(x)=x^{2}-3
f
(
x
)
=
x
2
−
3
, find the slope of the tangent line at
x
=
12
x=12
x
=
12
.
\newline
Answer:
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For the function
f
(
x
)
=
x
2
−
4
f(x)=x^{2}-4
f
(
x
)
=
x
2
−
4
, find the slope of the tangent line at
x
=
1
x=1
x
=
1
.
\newline
Answer:
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For the function
f
(
x
)
=
x
2
+
2
f(x)=x^{2}+2
f
(
x
)
=
x
2
+
2
, find the slope of the tangent line at
x
=
−
1
x=-1
x
=
−
1
.
\newline
Answer:
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For the function
f
(
x
)
=
2
x
−
6
f(x)=2 x-6
f
(
x
)
=
2
x
−
6
, find the slope of the tangent line at
x
=
−
6
x=-6
x
=
−
6
.
\newline
Answer:
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For the function
f
(
x
)
=
−
8
x
2
+
9
x
+
9
f(x)=-8 x^{2}+9 x+9
f
(
x
)
=
−
8
x
2
+
9
x
+
9
, find the slope of the tangent line at
x
=
9
x=9
x
=
9
.
\newline
Answer:
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For the function
f
(
x
)
=
3
x
2
+
7
x
+
4
f(x)=3 x^{2}+7 x+4
f
(
x
)
=
3
x
2
+
7
x
+
4
, find the slope of the tangent line at
x
=
6
x=6
x
=
6
.
\newline
Answer:
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For the function
f
(
x
)
=
−
7
x
2
+
3
x
−
5
f(x)=-7 x^{2}+3 x-5
f
(
x
)
=
−
7
x
2
+
3
x
−
5
, find the slope of the tangent line at
x
=
3
x=3
x
=
3
.
\newline
Answer:
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For the function
f
(
x
)
=
x
2
−
8
f(x)=x^{2}-8
f
(
x
)
=
x
2
−
8
, find the slope of the tangent line at
x
=
−
6
x=-6
x
=
−
6
.
\newline
Answer:
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For the function
f
(
x
)
=
x
2
−
4
f(x)=x^{2}-4
f
(
x
)
=
x
2
−
4
, find the slope of the tangent line at
x
=
3
x=3
x
=
3
.
\newline
Answer:
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For the function
f
(
x
)
=
x
2
−
11
f(x)=x^{2}-11
f
(
x
)
=
x
2
−
11
, find the slope of the tangent line at
x
=
12
x=12
x
=
12
.
\newline
Answer:
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For the function
f
(
x
)
=
11
x
2
+
12
x
+
9
f(x)=11 x^{2}+12 x+9
f
(
x
)
=
11
x
2
+
12
x
+
9
, find the slope of the tangent line at
x
=
−
9
x=-9
x
=
−
9
.
\newline
Answer:
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For the function
f
(
x
)
=
−
6
x
−
9
f(x)=-6 x-9
f
(
x
)
=
−
6
x
−
9
, find the slope of the tangent line at
x
=
1
x=1
x
=
1
.
\newline
Answer:
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For the function
f
(
x
)
=
−
6
x
2
+
9
x
+
2
f(x)=-6 x^{2}+9 x+2
f
(
x
)
=
−
6
x
2
+
9
x
+
2
, find the slope of the tangent line at
x
=
2
x=2
x
=
2
.
\newline
Answer:
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For the function
f
(
x
)
=
x
2
+
3
f(x)=x^{2}+3
f
(
x
)
=
x
2
+
3
, find the slope of the secant line between
x
=
2
x=2
x
=
2
and
x
=
4
x=4
x
=
4
.
\newline
Answer:
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For the function
f
(
x
)
=
x
2
−
4
f(x)=x^{2}-4
f
(
x
)
=
x
2
−
4
, find the slope of the secant line between
x
=
−
4
x=-4
x
=
−
4
and
x
=
−
1
x=-1
x
=
−
1
.
\newline
Answer:
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For the function
f
(
x
)
=
x
2
−
7
f(x)=x^{2}-7
f
(
x
)
=
x
2
−
7
, find the slope of the secant line between
x
=
−
6
x=-6
x
=
−
6
and
x
=
−
4
x=-4
x
=
−
4
.
\newline
Answer:
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For the function
f
(
x
)
=
x
2
−
6
f(x)=x^{2}-6
f
(
x
)
=
x
2
−
6
, find the slope of the secant line between
x
=
−
3
x=-3
x
=
−
3
and
x
=
−
1
x=-1
x
=
−
1
.
\newline
Answer:
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Which of the following is a correct interpretation of the expression
\newline
−
4
+
13
-4+13
−
4
+
13
?
\newline
Choose
1
1
1
answer:
\newline
(A) The number that is
4
4
4
to the left of
−
13
-13
−
13
on the number line
\newline
(B) The number that is
4
4
4
to the right of
−
13
-13
−
13
on the number line
\newline
(C) The number that is
13
13
13
to the left of
−
4
-4
−
4
on the number line
\newline
(D) The number that is
13
13
13
to the right of
−
4
-4
−
4
on the number line
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