Question is in attachment.
limit f(x) / x² = 2 when x tends to zero then evaluate.
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Answer:
Correct option is
A
x→0
lim
[f(x)]=0
C
x→0
lim
[
x
f(x)
] does not exist
Since x
2
> 0 and limit equals 2, f(x) must be a positive quantity.
Also, since
x→0
lim
x
2
f(x)
=2, denominator → zero and limit is finite.
Therefore, f(x) must be approaching 0 or lim
x→0
f(x)=0
+
.
Hence,
x→0
lim
[f(x)]=0.
x→0
+
lim
[
x
f(x)
]=
x→0
+
lim
[x
x
2
f(x)
]=0
and
x→0
−
lim
[
x
f(x)
]
=
x→0
−
lim
[x
x
2
f(x)
]=−1
Hence,
x→0
lim
[
x
f(x)
] does n
Step-by-step explanation:
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