lim x=2 Xpower2 3X +4/Xpower2-3
find limits
Answers
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Answer:
We have,
x→2
lim
x
4
−8x
2
+16
x
3
−3x
2
+4
=
x→2
lim
x
4
−8x
2
+4
2
x
3
−3x
2
+4
Solve,
Numerator
then, put x=2,
2
3
−3×2
2
+4=0
Divide x−2)x
3
−3x
2
+4(x
2
−x−2
x
3
−2x
2
_______________
−x
2
+4
−x
2
+2x
______________
−2x+4
−2x+4
____________
0
Now, x
3
−3x
2
+4=(x−2)(x
2
−x−2)
x→2
lim
x
4
−8x
2
+4
2
x
3
−3x
2
+4
=
x→2
lim
(x
2
−4
2
)
(x−2)(x
2
−x−2)
=
x→2
lim
(x
2
−4)(x
2
−4)
(x−2)(x
2
−(2−1)x−2)
=
x→2
lim
(x
2
−2
2
)(x
2
−2
2
)
(x−2)(x
2
−2x+1x−2)
=
x→2
lim
(x−2)(x+2)(x−2)(x+2)
(x−2)(x(x−2)+1(x−2))
=
x→2
lim
x−2)(x−2)(x+2)(x+2)
(x−2)(x−2)(x+1)
=
x→2
lim
(x+2)(x+2)
x+1
Now, taking limit and we get
=
(2+2)(2+2)
2+1
=
4×4
3
=
16
3
Hence, this is the answer.
