2-√x/4-x
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Answer:
How do you evaluate the limit
√
x
+
4
−
2
x
as x approaches
0
?
Calculus Determining Limits Algebraically
1 Answer
Lovecraft
Dec 9, 2016
lim
x
→
0
√
x
+
4
−
2
x
=
1
4
Explanation:
Multiply the numerator and the denominator by
√
x
+
4
+
2
lim
x
→
0
√
x
+
4
−
2
x
=
lim
x
→
0
√
x
+
4
−
2
x
⋅
√
x
+
4
+
2
√
x
+
4
+
2
Since
(
a
−
b
)
(
a
+
b
)
=
a
2
−
b
2
we have
lim
x
→
0
x
+
4
−
4
x
(
√
x
+
4
+
2
)
=
lim
x
→
0
x
x
(
√
x
+
4
+
2
)
=
lim
x
→
0
1
√
x
+
4
+
2
=
1
√
0
+
4
+
2
=
1
2
+
2
=
1
4
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