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Mathematics
Problem
Let
k
k
k
be a nonzero constant. Which expression is the second-degree Taylor polynomial centered at
x
=
0
x=0
x
=
0
for
ln
(
1
+
k
x
)
\ln(1+kx)
ln
(
1
+
k
x
)
? a)
k
x
+
k
2
x
2
2
kx+\dfrac{k^{2}x^{2}}{2}
k
x
+
2
k
2
x
2
b)
k
x
−
k
2
x
2
2
kx-\dfrac{k^{2}x^{2}}{2}
k
x
−
2
k
2
x
2
c)
1
+
k
x
−
k
2
x
2
2
1+kx-\dfrac{k^{2}x^{2}}{2}
1
+
k
x
−
2
k
2
x
2
d)
k
x
−
k
2
x
2
kx-k^{2}x^{2}
k
x
−
k
2
x
2
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