Dam hai to solve karke dikhao...Bahut sare points milenge...
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Answers
Answer:
The limit does not exist.
Explanation:
Assume for the moment that x approaches 0 from the positive side.
Then we want
lim
x
→
0
+
e
1
x
e
1
x
+
1
.
Let
y
=
1
x
, and the above equals
lim
y
→
∞
e
y
e
y
+
1
.
The numerator and denominator approach infinity. Applying L'Hopital's Rule, take the derivatives of the numerator and denominator. Then the above equals:
lim
y
→
∞
e
y
e
y
=
lim
y
→
∞
1
=
1
.
Now assume that x approaches 0 from the negative side.
Then
lim
x
→
0
−
e
1
x
e
1
x
+
1
.
=
lim
y
→
−
∞
e
y
e
y
+
1
.
The exponentials go to zero, and the denominator goes to 1.
=
0
0
+
1
=
0
.
Since the left- and right- and limits are not equal, the limit does not exist.
Answer:
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