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Mathematics
Mathematics
Problem
The function
f
f
f
is defined by
f
(
x
)
=
{
k
x
2
+
3
,
x
=
1
,
x
2
+
3
,
x
≠
1.
f(x)=\begin{cases} kx^{2}+3, & x=1,\\ x^{2}+3, & x\neq 1. \end{cases}
f
(
x
)
=
{
k
x
2
+
3
,
x
2
+
3
,
x
=
1
,
x
=
1.
For which value of
k
k
k
is
f
f
f
continuous at
x
=
1
x=1
x
=
1
, and what is
lim
x
→
1
f
(
x
)
\displaystyle \lim_{x\to 1} f(x)
x
→
1
lim
f
(
x
)
? a)
k
=
4
,
lim
=
4
k=4,\;\lim =4
k
=
4
,
lim
=
4
b)
k
=
1
,
lim
=
3
k=1,\;\lim =3
k
=
1
,
lim
=
3
c)
k
=
1
,
lim
=
4
k=1,\;\lim =4
k
=
1
,
lim
=
4
d)
k
=
0
,
lim
=
3
k=0,\;\lim =3
k
=
0
,
lim
=
3
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