Answer:
According to given question,
(x
2
+x(f(x)−2)+2
3
−3−
f(x))=0
⇒f(x)[
−x]=x
−2x+2
−3
⇒f(x)=
−x
x
............(1)
It is given that, function is continuous, Hence limit will be equal to the value at x=
,
Therefore,
Lim
x→
f(x)=f(
)...........(2)
Solving limit using L.hospital's rule (i.e. derivative approach)
=> Lim
f(x)=
−1
2x−2
..................From(1)
=> f(
)=2−2
................................From(2)
=2(1−
)
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Answers & Comments
Answer:
According to given question,
(x
2
+x(f(x)−2)+2
3
−3−
3
f(x))=0
⇒f(x)[
3
−x]=x
2
−2x+2
3
−3
⇒f(x)=
3
−x
x
2
−2x+2
3
−3
............(1)
It is given that, function is continuous, Hence limit will be equal to the value at x=
3
,
Therefore,
Lim
x→
3
f(x)=f(
3
)...........(2)
Solving limit using L.hospital's rule (i.e. derivative approach)
=> Lim
x→
3
f(x)=
−1
2x−2
..................From(1)
=> f(
3
)=2−2
3
................................From(2)
=2(1−
3
)