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Mathematics
Mathematics
Problem
Discuss the continuity of the function
f
(
x
)
=
lim
n
→
∞
log
(
2
+
x
)
−
x
2
n
sin
x
1
+
x
2
n
at
x
=
1
f(x) = \lim_{n \to \infty} \frac{\log(2+x) - x^{2n} \sin x}{1+x^{2n}} \quad \text{at } x = 1
f
(
x
)
=
n
→
∞
lim
1
+
x
2
n
lo
g
(
2
+
x
)
−
x
2
n
sin
x
at
x
=
1
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