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Math Problems
Grade 8
Write variable expressions for arithmetic sequences
Let
h
(
x
)
=
{
x
+
26
−
5
x
+
1
for
x
≥
−
26
,
x
≠
−
1
k
for
x
=
−
1
h(x)=\left\{\begin{array}{ll}\frac{\sqrt{x+26}-5}{x+1} & \text { for } x \geq-26, x \neq-1 \\ k & \text { for } x=-1\end{array}\right.
h
(
x
)
=
{
x
+
1
x
+
26
−
5
k
for
x
≥
−
26
,
x
=
−
1
for
x
=
−
1
\newline
h
h
h
is continuous for all
x
>
−
26
x>-26
x
>
−
26
.
\newline
What is the value of
k
k
k
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
1
5
-\frac{1}{5}
−
5
1
\newline
(B)
1
1
1
\newline
(C)
1
10
\frac{1}{10}
10
1
\newline
(D)
0
0
0
Get tutor help
f
(
x
)
=
{
sin
(
x
⋅
π
)
for
−
8
<
x
<
0
x
5
for
0
≤
x
≤
10
f(x)=\left\{\begin{array}{ll} \sin (x \cdot \pi) & \text { for }-8<x<0 \\ \frac{x}{5} & \text { for } 0 \leq x \leq 10 \end{array}\right.
f
(
x
)
=
{
sin
(
x
⋅
π
)
5
x
for
−
8
<
x
<
0
for
0
≤
x
≤
10
\newline
Find
lim
x
→
−
5
f
(
x
)
\lim _{x \rightarrow-5} f(x)
lim
x
→
−
5
f
(
x
)
.
\newline
Choose
1
1
1
answer:
\newline
(A)
−
1
-1
−
1
\newline
(B)
0
0
0
\newline
(C)
1
1
1
\newline
(D) The limit doesn't exist.
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