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Math Problems
Calculus
Find derivatives of exponential functions
There is an exponential function that is
y
y
y
positive and decreasing. Two coordinates are
(
0
,
3600
)
(0, 3600)
(
0
,
3600
)
and
(
2
,
225
)
(2,225)
(
2
,
225
)
. What is the equation
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There is an exponential function that is
y
y
y
positive and decreasing. Two coordinates are
(
0
,
3600
)
(0, 3600)
(
0
,
3600
)
and
(
2
,
225
)
(2,225)
(
2
,
225
)
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f
(
x
)
=
3
x
2
f(x)=3 x^{2}
f
(
x
)
=
3
x
2
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Find the solution interval for the inequality:
\newline
ln
(
x
2
+
2
)
≤
6.2
\ln \left(x^{2}+2\right) \leq 6.2
ln
(
x
2
+
2
)
≤
6.2
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Solve for the Surface Area of the figure below
\newline
Hint: Find the missing side of the base
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How does the value of
a
a
a
in each function affect its graph?
\newline
1
1
1
.
g
(
x
)
=
4
x
2
g(x)=4 x^{2}
g
(
x
)
=
4
x
2
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Find the exact coordinates of the turning points on the curve
y
=
sin
3
x
cos
x
y=\sin^3 x\cos x
y
=
sin
3
x
cos
x
for
0
0
0
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What is the period of the function
\newline
g
(
x
)
=
−
sin
(
−
8
x
−
3
)
+
5
g(x)=-\sin(-8x-3)+5
g
(
x
)
=
−
sin
(
−
8
x
−
3
)
+
5
?
\newline
Give an exact value.
\newline
□
\square
□
units
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The circle has center
O
O
O
, and the measure of angle
ROS
\operatorname{ROS}
ROS
is
15
0
∘
150^{\circ}
15
0
∘
. The length of minor arc
R
S
undefined
\widehat{R S}
RS
is what fraction of the circumference of the circle?
\newline
(The number of degrees of arc in a circle is
360
360
360
.)
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find the derivative
d
d
x
(
e
x
sin
(
x
)
)
\frac{d}{dx}(e^{x}\sin(x))
d
x
d
(
e
x
sin
(
x
))
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15
15
15
. Use the first derivative test to find and classify all local extrema in the interval
(
0
,
4
)
(0,4)
(
0
,
4
)
for the function
\newline
f
(
x
)
=
−
3
x
4
ln
(
3
x
)
f(x)=-3 x^{4} \ln (3 x)
f
(
x
)
=
−
3
x
4
ln
(
3
x
)
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Evaluate
∑
m
≥
1
(
sin
(
sin
(
m
!
)
)
)
m
\sum_{m \geq 1}(\sin(\sin(m!)))^{m}
∑
m
≥
1
(
sin
(
sin
(
m
!))
)
m
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sin
(
x
)
=
cos
(
x
)
\sin(x) = \cos(x)
sin
(
x
)
=
cos
(
x
)
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if
g
(
x
)
=
2
x
2
+
x
g(x)=2x^2+x
g
(
x
)
=
2
x
2
+
x
what is the value of
g
(
1
2
)
g(\frac{1}{2})
g
(
2
1
)
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Find the derivative of
f
(
x
)
f(x)
f
(
x
)
.
\newline
f
(
x
)
=
e
(
x
+
1
)
f(x)=e^{(x+1)}
f
(
x
)
=
e
(
x
+
1
)
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find the first derivative of
sin
(
4
X
)
\sin(4X)
sin
(
4
X
)
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The graph showrs the proportional relationship. Derive the equation of the line
\newline
y
=
m
x
y=mx
y
=
m
x
through the origin.
\newline
(
1
1
1
point)
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Find the derivative
f
(
x
)
=
e
(
x
+
1
)
f(x)=e^{(x+1)}
f
(
x
)
=
e
(
x
+
1
)
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If
f
(
x
)
=
2
x
3
−
2
,
f(x)=2x^3-2,
f
(
x
)
=
2
x
3
−
2
,
what is the value of
f
(
2
)
?
f(2)?
f
(
2
)?
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If
f
(
x
)
=
2
x
3
−
2
,
f(x)=2x^3-2,
f
(
x
)
=
2
x
3
−
2
,
what is the value of
f
(
2
)
?
f(2)?
f
(
2
)?
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Find the derivative of
\newline
f
(
x
)
f(x)
f
(
x
)
.
\newline
f
(
x
)
=
e
(
x
+
1
)
f(x)=e^{(x+1)}
f
(
x
)
=
e
(
x
+
1
)
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Find the derivative of
\newline
f
(
x
)
f(x)
f
(
x
)
.
\newline
f
(
x
)
=
x
e
x
f(x)=xe^{x}
f
(
x
)
=
x
e
x
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Find the derivative
\newline
2
(
x
2
+
4
)
2(x^{2}+4)
2
(
x
2
+
4
)
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y
=
3
7
x
−
12
7
y=\frac{3}{7} x-\frac{12}{7}
y
=
7
3
x
−
7
12
\newline
What is the slope of the graph of the given equation?
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Find the derivative of
f
(
x
)
f(x)
f
(
x
)
.
\newline
f
(
x
)
=
e
x
f(x) = e^x
f
(
x
)
=
e
x
\newline
f
′
(
x
)
=
f'\left(x\right) =
f
′
(
x
)
=
______
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