Prove continuity of |x-1| + |x+1| at x not equal to -1 & 1.
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Prove continuity of |x-1| + |x+1| at x not equal to -1 & 1.
Prove continuity of |x-1| + |x+1| at x not equal to -1 & 1.
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Answer:
f(x)=
e
1/x
+1
e
1/x
−1
f(x)
x→0
−
=lim
h→0
e
−1/h
+1
e
−1/h
−1
f(x)
x→0
−
=lim
h→0
e
1/h
1
+1
e
1/h
1
−1
=
0+1
0−1
=−1
f(x)
x→0
+
=lim
h→0
e
1/h
+1
e
1/h
−1
f(x)
x→0
+
=lim
h→0
1−
e
1/h
1
1−
e
1/h
1
=
1+0
1−0
=1
f(x)
x→0
−
=f(x)
x→0
+
L.H.L is not equal to R.H.L at x=0.
So, function is not continuous at x=0.
Answer:
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