lim x->3 x-3/x-(√3+√2)√x+√6
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Answered by
6
Answer:
the function is indeterminate
0
0
when x = 3
Multiply the numerator/denominator by the conjugate of the numerator.
√
x
+
6
−
x
conjugate
→
√
x
+
6
+
x
⇒
(
√
x
+
6
−
x
)
(
√
x
+
6
+
x
)
(
x
−
3
)
(
√
x
+
6
+
x
)
=
x
+
6
−
x
2
(
x
−
3
)
(
√
x
+
6
+
x
)
=
−
(
x
−
3
)
(
x
+
2
)
(
x
−
3
)
(
√
x
+
6
+
x
)
exclusion x ≠ 3
=
−
(
x
+
2
)
√
x
+
6
+
x
⇒
lim
x
→
3
√
x
+
6
−
x
x
−
3
=
lim
x
→
3
−
(
x
+
2
)
√
x
+
6
+
x
=
−
5
6
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