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Mathematics
Mathematics
Problem
y
=
f
(
x
)
y = f(x)
y
=
f
(
x
)
is a function which satisfies (i)
f
(
0
)
=
0
f(0) = 0
f
(
0
)
=
0
(ii)
f
′
′
(
x
)
=
f
′
(
x
)
f''(x) = f'(x)
f
′′
(
x
)
=
f
′
(
x
)
and (iii)
f
′
(
0
)
=
1
f'(0) = 1
f
′
(
0
)
=
1
Then, the area bounded by the graph of
y
=
f
(
x
)
y = f(x)
y
=
f
(
x
)
, the lines
x
=
0
,
x
−
1
=
0
x = 0, x - 1 = 0
x
=
0
,
x
−
1
=
0
and
y
+
1
=
0
y + 1 = 0
y
+
1
=
0
, is a.
e
e
e
b.
e
−
2
e - 2
e
−
2
c.
e
−
1
e - 1
e
−
1
d.
e
+
1
e + 1
e
+
1
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