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Problems
Define
f
(
x
)
=
{
sin
(
x
−
1
)
x
−
1
,
x
<
1
d
,
x
=
1
b
x
+
2
,
x
>
1
f(x)=\begin{cases}\dfrac{\sin(x-1)}{x-1},& x<1\\d,& x=1\\bx+2,& x>1\end{cases}
f
(
x
)
=
⎩
⎨
⎧
x
−
1
sin
(
x
−
1
)
,
d
,
b
x
+
2
,
x
<
1
x
=
1
x
>
1
…
Mathematics
Problem
Define
f
(
x
)
=
{
sin
(
x
−
1
)
x
−
1
,
x
<
1
d
,
x
=
1
b
x
+
2
,
x
>
1
f(x)=\begin{cases}\dfrac{\sin(x-1)}{x-1},& x<1\\d,& x=1\\bx+2,& x>1\end{cases}
f
(
x
)
=
⎩
⎨
⎧
x
−
1
sin
(
x
−
1
)
,
d
,
b
x
+
2
,
x
<
1
x
=
1
x
>
1
Which ordered pair
(
b
,
d
)
(b,d)
(
b
,
d
)
ensures that
f
f
f
is continuous at
x
=
1
x=1
x
=
1
? a)
(
1
,
1
)
(1,1)
(
1
,
1
)
b)
(
−
2
,
0
)
(-2,0)
(
−
2
,
0
)
c)
(
−
1
,
1
)
(-1,1)
(
−
1
,
1
)
d)
(
−
1
,
−
1
)
(-1,-1)
(
−
1
,
−
1
)
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