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Math Problems
Calculus
Find limits involving trigonometric functions
give me the roots of
(
2
x
−
1
)
(
x
−
5
)
(
x
+
2
)
=
0
(2x - 1)(x - 5)(x + 2) = 0
(
2
x
−
1
)
(
x
−
5
)
(
x
+
2
)
=
0
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Is
(
−
5
,
6
)
(-5, 6)
(
−
5
,
6
)
a solution to this system of equations?
\newline
15
x
+
14
y
=
9
15x + 14y = 9
15
x
+
14
y
=
9
\newline
18
x
+
18
y
=
18
18x + 18y = 18
18
x
+
18
y
=
18
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y
−
(
−
3
y
)
=
y - (-3y) =
y
−
(
−
3
y
)
=
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How many solutions does the system of equations below have?
10
x
−
7
y
=
−
10
10x - 7y = -10
10
x
−
7
y
=
−
10
20
x
−
14
y
=
−
20
20x - 14y = -20
20
x
−
14
y
=
−
20
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Which sign makes the statement true?
\newline
10
12
−
1
12
\frac{10}{12} - \frac{1}{12}
12
10
−
12
1
?
11
12
\frac{11}{12}
12
11
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
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Find the solution of the system of equations.
5
x
+
10
y
=
−
5
5x+10y=-5
5
x
+
10
y
=
−
5
and
−
5
x
−
y
=
32
-5x-y=32
−
5
x
−
y
=
32
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Given
F
(
x
)
=
−
3
x
+
5
F(x)=-3x+5
F
(
x
)
=
−
3
x
+
5
, find
f
(
−
2
)
f(-2)
f
(
−
2
)
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Which sign makes the statement true?
\newline
2
1
7
2\frac{1}{7}
2
7
1
?
\text{?}
?
2
6
7
2\frac{6}{7}
2
7
6
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
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Evaluate the function:
f
(
x
)
=
−
3
x
+
1
[
−
2
,
2
]
f(x)=-3x+1\quad[-2,2]
f
(
x
)
=
−
3
x
+
1
[
−
2
,
2
]
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Solve for
x
x
x
\newline
5
x
+
x
=
12
5x+x = 12
5
x
+
x
=
12
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Solve the inequality for
x
x
x
in terms of
y
y
y
.
\newline
x
−
3
y
≥
−
7
x-3y \geq -7
x
−
3
y
≥
−
7
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Find a point on the line and the line's slope.
\newline
y
+
4
=
3
(
x
+
3
)
y+4=3(x+3)
y
+
4
=
3
(
x
+
3
)
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y
=
−
2
x
+
4
y=-2x+4
y
=
−
2
x
+
4
\newline
Complete the missing value in the solution to the equation.
\newline
( _____ , -2)
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∬
D
(
2
x
+
y
)
d
x
d
y
,
D
:
x
+
y
=
3
;
y
=
0
;
x
=
0
\iint_{D}(2 x+y) d x d y, D: x+y=3 ; y=0 ; x=0
∬
D
(
2
x
+
y
)
d
x
d
y
,
D
:
x
+
y
=
3
;
y
=
0
;
x
=
0
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Compare the numbers. Pick the correct sign.
\newline
−
5
?
−
8
-5 \,?\, -8
−
5
?
−
8
\newline
\newline
You can use the number line to help.
\newline
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
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If
f
(
x
)
=
5
x
−
3
f(x)=5x-3
f
(
x
)
=
5
x
−
3
, what is the value of
f
(
4
)
f(4)
f
(
4
)
?
\newline
□
\square
□
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Evaluate the following limit using L'Hospital's rule.
\newline
lim
x
→
0
+
(
9
x
)
sin
(
5
x
)
\lim _{x \rightarrow 0^{+}}(9 x)^{\sin (5 x)}
x
→
0
+
lim
(
9
x
)
s
i
n
(
5
x
)
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Solve for a positive value of
x
x
x
.
\newline
log
3
(
243
)
=
x
\log _{3}(243)=x
lo
g
3
(
243
)
=
x
\newline
Answer:
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x
÷
3
=
10
x \div 3=10
x
÷
3
=
10
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k
4
+
3
=
14
\frac{k}{4}+3=14
4
k
+
3
=
14
\newline
What is the value of
k
k
k
in the equation shown?
\newline
□
\square
□
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lim
x
→
0
(
csc
2
x
−
1
2
x
)
=
\lim _{x \rightarrow 0}\left(\csc 2 x-\frac{1}{2 x}\right)=
lim
x
→
0
(
csc
2
x
−
2
x
1
)
=
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d
y
d
x
=
2
y
2
\frac{dy}{dx} = 2y^2
d
x
d
y
=
2
y
2
and
y
(
1
)
=
−
1
y(1)=-1
y
(
1
)
=
−
1
.
y
(
3
)
=
?
y(3)=?
y
(
3
)
=
?
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x
+
2
x
=
13
x+2x=13
x
+
2
x
=
13
what is value of
x
x
x
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f
(
x
)
=
sin
2
x
cos
x
f(x)=\sin 2 x \cos x
f
(
x
)
=
sin
2
x
cos
x
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y
=
−
9
(
x
+
1
)
(
x
+
1
)
y=-9(x+1)(x+1)
y
=
−
9
(
x
+
1
)
(
x
+
1
)
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3
x
−
y
=
7
3 x-y=7
3
x
−
y
=
7
find
y
y
y
when
x
x
x
is
7
7
7
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a)
−
7
=
x
+
3
-7=x+3
−
7
=
x
+
3
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Using implicit differentiation, find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
.
\newline
y
cos
(
3
x
+
5
y
)
=
−
3
x
y
−
3
y \cos (3 x+5 y)=-3 x y-3
y
cos
(
3
x
+
5
y
)
=
−
3
x
y
−
3
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What value of
w
w
w
is a solution to this equation?
\newline
w
−
4
=
2
w - 4 = 2
w
−
4
=
2
\newline
Choices:
\newline
(A)
w
=
4
w = 4
w
=
4
\newline
(B)
w
=
6
w = 6
w
=
6
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Determine whether the point
(
3
,
1
)
(3,1)
(
3
,
1
)
is a solution to the equation
4
x
−
2
y
=
6
4 x-2 y=6
4
x
−
2
y
=
6
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Evaluate
∑
m
≥
0
sin
(
m
π
+
π
m
+
1
)
\sum_{m \geq 0}\sin(m \pi+\frac{\pi}{m+1})
∑
m
≥
0
sin
(
mπ
+
m
+
1
π
)
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x
−
5
≤
2
x-5 \leq 2
x
−
5
≤
2
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Which value for the constant
d
d
d
makes
x
=
−
3
x=-3
x
=
−
3
an extraneous solution in the following equation?
25
+
3
x
=
d
+
2
x
\sqrt{25+3x}=d+2x
25
+
3
x
=
d
+
2
x
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Question
\newline
Asomme that () is a positive acute angle
\newline
Giveni
cos
θ
=
4
5
\cos \theta=\frac{4}{5}
cos
θ
=
5
4
\newline
Find:
sin
90
\sin 90
sin
90
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How many solutions does the given system of equations have?
\newline
y
−
7
=
−
6
(
x
+
1
)
y-7=-6(x+1)
y
−
7
=
−
6
(
x
+
1
)
\newline
4
y
+
24
x
+
28
=
0
4y+24x+28=0
4
y
+
24
x
+
28
=
0
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Determine the largest integer value of
x
x
x
in the solution of the following inequality.
\newline
−
2
x
+
8
>
20
-2 x+8>20
−
2
x
+
8
>
20
\newline
Answer:
x
=
x=
x
=
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Determine the largest integer value of
x
x
x
in the solution of the following inequality.
\newline
4
x
+
7
<
1
4 x+7<1
4
x
+
7
<
1
\newline
Answer:
x
=
x=
x
=
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Determine the smallest integer value of
x
x
x
in the solution of the following inequality.
\newline
4
x
+
6
>
4
4 x+6>4
4
x
+
6
>
4
\newline
Answer:
x
=
x=
x
=
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lim
x
→
0
(
sin
3
x
sin
2
x
)
=
□
\lim_{x \to 0}\left(\frac{\sin 3x}{\sin 2x}\right)= \square
x
→
0
lim
(
sin
2
x
sin
3
x
)
=
□
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Which value of
x
x
x
satisfies the equation
5
2
(
x
+
5
6
)
=
−
65
12
\frac{5}{2}\left(x+\frac{5}{6}\right)=-\frac{65}{12}
2
5
(
x
+
6
5
)
=
−
12
65
?
\newline
2
2
2
\newline
3
3
3
\newline
−
3
-3
−
3
\newline
−
2
-2
−
2
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Which value of
x
x
x
satisfies the equation
4
5
(
x
+
3
5
)
=
52
25
\frac{4}{5}\left(x+\frac{3}{5}\right)=\frac{52}{25}
5
4
(
x
+
5
3
)
=
25
52
?
\newline
−
2
-2
−
2
\newline
1
1
1
\newline
−
1
-1
−
1
\newline
2
2
2
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Which value of
x
x
x
satisfies the equation
1
3
(
x
−
1
2
)
=
−
1
2
\frac{1}{3}\left(x-\frac{1}{2}\right)=-\frac{1}{2}
3
1
(
x
−
2
1
)
=
−
2
1
?
\newline
1
1
1
\newline
2
2
2
\newline
−
2
-2
−
2
\newline
−
1
-1
−
1
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What value of
w
w
w
makes the equation below true?
\newline
8
w
+
8
=
88
8 w+8=88
8
w
+
8
=
88
\newline
9
9
9
\newline
10
10
10
\newline
11
11
11
\newline
88
88
88
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What value of
w
w
w
makes the equation below true?
\newline
8
w
−
5
=
3
8 w-5=3
8
w
−
5
=
3
\newline
1
1
1
\newline
4
4
4
\newline
6
6
6
\newline
8
8
8
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What value of
y
y
y
makes the equation below true?
\newline
6
y
−
1
=
17
6 y-1=17
6
y
−
1
=
17
\newline
3
3
3
\newline
6
6
6
\newline
15
15
15
\newline
16
16
16
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What value of
y
y
y
makes the equation below true?
\newline
4
y
−
5
=
23
4 y-5=23
4
y
−
5
=
23
\newline
6
6
6
\newline
7
7
7
\newline
14
14
14
\newline
23
23
23
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What value of
y
y
y
makes the equation below true?
\newline
2
y
+
5
=
21
2 y+5=21
2
y
+
5
=
21
\newline
5
5
5
\newline
8
8
8
\newline
14
14
14
\newline
16
16
16
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What value of
z
z
z
makes the equation below true?
\newline
10
z
+
5
=
75
10 z+5=75
10
z
+
5
=
75
\newline
7
7
7
\newline
10
10
10
\newline
11
11
11
\newline
15
15
15
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What value of
y
y
y
makes the equation below true?
\newline
9
y
−
2
=
25
9 y-2=25
9
y
−
2
=
25
\newline
2
2
2
\newline
3
3
3
\newline
5
5
5
\newline
9
9
9
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Solve the differential equation.
\newline
d
y
d
x
=
e
2
x
−
2
y
\frac{dy}{dx}=e^{2x-2y}
d
x
d
y
=
e
2
x
−
2
y
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