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Math Problems
Calculus
Quotient rule
Find the unknown number in each equation:
\newline
r
8
=
12
\frac{r}{8}=12
8
r
=
12
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Evaluate:
f
(
x
,
y
)
=
x
cos
y
+
y
sin
x
f(x,y) = x\cos y + y\sin x
f
(
x
,
y
)
=
x
cos
y
+
y
sin
x
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Solve:
lim
x
→
4
x
x
−
4
\lim_{x \rightarrow 4}\frac{x}{x-4}
x
→
4
lim
x
−
4
x
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Find the derivative of
f
(
x
)
=
5
x
3
+
5
x
2
−
30
f(x) = 5x^3+5x^2-30
f
(
x
)
=
5
x
3
+
5
x
2
−
30
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g
(
x
)
=
2
x
−
1
g(x) = 2^{x} - 1
g
(
x
)
=
2
x
−
1
for
−
8
≤
x
<
1
-8 \leq x < 1
−
8
≤
x
<
1
;
x
\sqrt{x}
x
for
x
≥
1
x \geq 1
x
≥
1
\newline
Find
lim
x
→
4
g
(
x
)
\lim_{x \to 4} g(x)
lim
x
→
4
g
(
x
)
.
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Force equals mass times acceleration.
\newline
F
=
m
a
\mathrm{F}=\mathrm{ma}
F
=
ma
\newline
Solve the equation for the mass,
m
m
m
.
\newline
m
=
□
□
\mathrm{m}=\frac{\square}{\square}
m
=
□
□
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Find the derivative of
h
(
x
)
=
(
x
2
+
x
tan
(
x
)
)
h(x)=(\frac{x^2+x}{\tan(x)})
h
(
x
)
=
(
t
a
n
(
x
)
x
2
+
x
)
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what is derivative of
sin
\sin
sin
?
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The particular solution of the differential equation
d
y
d
x
−
e
x
=
y
e
x
\frac{dy}{dx}-e^{x}=ye^{x}
d
x
d
y
−
e
x
=
y
e
x
, when
x
=
0
x=0
x
=
0
and
y
=
1
y=1
y
=
1
is
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f
(
x
)
=
x
+
2
x
2
−
1
f(x)=\frac{x+2}{x^2-1}
f
(
x
)
=
x
2
−
1
x
+
2
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Evaluate the limit
lim
x
→
∞
(
x
2
e
4
x
−
1
−
4
x
)
\lim_{x \to \infty}\left(\frac{x^{2}}{e^{4x}-1-4x}\right)
x
→
∞
lim
(
e
4
x
−
1
−
4
x
x
2
)
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Find the argument of the complex number
2
+
2
i
2+2 i
2
+
2
i
in the interval
0
≤
θ
<
2
π
0 \leq \theta<2 \pi
0
≤
θ
<
2
π
. Express your answer in terms of
π
\pi
π
.
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Evaluate
∫
x
2
e
2
x
d
x
\int x^{2}e^{2x}dx
∫
x
2
e
2
x
d
x
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Find
f
′
(
x
)
f'(x)
f
′
(
x
)
where
f
(
x
)
=
−
2
x
cos
(
x
)
f(x)=-2x\cos(x)
f
(
x
)
=
−
2
x
cos
(
x
)
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What was the initial speed of a car if its speed is
40
m
s
40\frac{m}{s}
40
s
m
after
5
5
5
seconds of accelerating at
4
m
s
2
4\frac{m}{s^2}
4
s
2
m
?
\newline
A.
20
m
s
20\frac{m}{s}
20
s
m
\newline
B.
60
m
s
60\frac{m}{s}
60
s
m
\newline
C.
10
m
s
10\frac{m}{s}
10
s
m
\newline
D.
25
m
s
25\frac{m}{s}
25
s
m
\newline
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f
(
x
)
=
x
e
x
f(x)=xe^{x}
f
(
x
)
=
x
e
x
\newline
f
′
(
x
)
=
?
f'(x) =?
f
′
(
x
)
=
?
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Find the derivative of
f
(
x
)
f(x)
f
(
x
)
f
(
x
)
=
e
(
x
+
1
)
f(x)=e^{(x+1)}
f
(
x
)
=
e
(
x
+
1
)
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d
y
d
t
+
5
y
(
t
)
=
x
(
t
)
\frac{dy}{dt}+5y(t)=x(t)
d
t
d
y
+
5
y
(
t
)
=
x
(
t
)
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Find integral of
x
x
x^x
x
x
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What is the discriminant of the quadratic equation
7
x
2
−
x
−
6
=
0
7 x^{2}-x-6=0
7
x
2
−
x
−
6
=
0
?
\newline
169
169
169
\newline
167
167
167
\newline
−
169
-169
−
169
\newline
−
167
-167
−
167
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15
m/s
=
4
π
rad/s
×
r
×
sin
(
1
5
∘
)
15\,\text{m/s} = 4\pi\,\text{rad/s} \times r \times \sin(15^\circ)
15
m/s
=
4
π
rad/s
×
r
×
sin
(
1
5
∘
)
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Which of the following is a correct interpretation of the expression
5
−
8
5-8
5
−
8
?
\newline
Choose
1
1
1
answer:
\newline
(A) Start at
5
5
5
on the number line and move
8
8
8
to the left.
\newline
(B) Start at
5
5
5
on the number line and move
8
8
8
to the right.
\newline
(C) Start at
8
8
8
on the number line and move
5
5
5
to the left.
\newline
(D) Start at
8
8
8
on the number line and move
5
5
5
to the right.
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Differentiate the given function using differentiation formulas
\newline
a.
\newline
f
(
x
)
=
sin
sin
(
4
x
+
7
x
4
)
f(x)=\sin \sin(4x+7x^{4})
f
(
x
)
=
sin
sin
(
4
x
+
7
x
4
)
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What is the slope of
y
=
−
4
x
−
3
y=-4 x-3
y
=
−
4
x
−
3
?
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What is the slope of
y
=
5
x
−
1
y=5 x-1
y
=
5
x
−
1
?
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What is the slope of
y
=
−
x
+
7
y=-x+7
y
=
−
x
+
7
?
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What is the slope of
y
=
4
−
2
x
y=4-2 x
y
=
4
−
2
x
?
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What is the slope of
y
=
−
1
+
3
x
y=-1+3 x
y
=
−
1
+
3
x
?
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What is the slope of
y
=
x
+
5
y=x+5
y
=
x
+
5
?
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What is the slope of
y
=
−
5
+
4
x
y=-5+4 x
y
=
−
5
+
4
x
?
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What is the slope of
y
=
−
4
y=-4
y
=
−
4
?
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Find the derivative of
r
(
x
)
r(x)
r
(
x
)
.
\newline
r
(
x
)
=
ln
(
1
x
)
r(x) = \ln\left(\frac{1}{x}\right)
r
(
x
)
=
ln
(
x
1
)
\newline
r
′
(
x
)
=
r'(x) =
r
′
(
x
)
=
______
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Find the derivative of
q
(
x
)
q(x)
q
(
x
)
.
\newline
q
(
x
)
=
ln
(
x
e
)
q(x) = \ln\left(\frac{x}{e}\right)
q
(
x
)
=
ln
(
e
x
)
\newline
q
′
(
x
)
=
q'\left(x\right) =
q
′
(
x
)
=
______
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Find the derivative of
h
(
x
)
h(x)
h
(
x
)
.
\newline
h
(
x
)
=
ln
(
x
2
)
h(x) = \ln(x^2)
h
(
x
)
=
ln
(
x
2
)
\newline
h
′
(
x
)
=
h'(x) =
h
′
(
x
)
=
______
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Find the derivative of
g
(
x
)
g(x)
g
(
x
)
.
\newline
g
(
x
)
=
ln
(
2
x
)
g(x) = \ln(2x)
g
(
x
)
=
ln
(
2
x
)
\newline
g
′
(
x
)
=
g^{\prime}(x) =
g
′
(
x
)
=
______
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Find the derivative of
f
(
x
)
f(x)
f
(
x
)
.
\newline
f
(
x
)
=
e
x
x
f(x) = \frac{e^x}{x}
f
(
x
)
=
x
e
x
\newline
f
′
(
x
)
=
f'(x) =
f
′
(
x
)
=
______
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