Question

Discuss the continuity of function f (x) = 2-x x <2 2+x when x is greater than or equal to 2
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Answer 1

Answer:

lim

x→2

−

f(x)=

h→0

lim

f(2−h)=

h→0

lim

∣2−h−2∣=

h→0

lim

∣−h∣=0

x→2

+

lim

f(x)=

h→0

lim

f(2+h)=

x→0

lim

∣2+h−2∣=∣h∣=0

and f(2)=∣2−2∣=0

⇒f is continuous at x=2.