find out( lim x tends to 4 )5+sqrt(x)/sqrt(5+x)
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0
Answer:
lim
x
→
4
3
−
√
5
+
x
x
−
4
and to
lim
x
→
4
x
−
4
1
−
√
5
−
x
but both in one expression.
So multiply
3
−
√
5
+
x
1
−
√
5
−
x
by
(
3
+
√
5
+
x
)
(
3
+
√
5
+
x
)
⋅
(
1
+
√
5
−
x
)
(
1
+
√
5
−
x
)
to get:
lim
x
→
4
(
9
−
(
5
+
x
)
)
(
1
+
√
5
−
x
)
(
3
+
√
5
+
x
)
(
1
−
(
5
−
x
)
)
=
lim
x
→
4
(
4
−
x
)
(
1
+
√
5
−
x
)
(
3
+
√
5
+
x
)
(
−
(
4
−
x
)
)
=
lim
x
→
4
−
(
1
+
√
5
−
x
)
3
+
√
5
+
x
=
−
(
1
+
√
1
)
3
+
√
9
=
−
2
6
=
−
1
3
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