lim X tends to infinity (x^1/2 - xln(1+1/x^1/2)
Answers
Answered by
1
Answer:
lim
x
→
∞
x
−
ln
(
x
2
+
1
)
=
+
∞
Explanation:
As
x
=
ln
e
x
, we can write the function as:
x
−
ln
(
x
2
+
1
)
=
ln
e
x
−
ln
(
x
2
+
1
)
Using the properties of logarithms then we have:
x
−
ln
(
x
2
+
1
)
=
ln
(
e
x
x
2
+
1
)
Now we know the the exponential is an infinite of higher order than any polynomial for
x
→
∞
, so
lim
x
→
∞
e
x
x
2
+
1
=
+
∞
and then as the logarithm is continuous in
(
0
,
+
∞
)
lim
x
→
∞
ln
(
e
x
x
2
+
1
)
=
+
∞
Mark me as brain list
Similar questions