Prove-that-f-x-x-2-is-continous-at-x-2-while-f-x-0-x-2-x-2-x-2-is-not-continous-at-x-2-

Question Number 10095 by Tawakalitu ayo mi last updated on 23/Jan/17

Prove that f (x) = x^{2} is continous at x = 2

while f (x) = {_{0 x = 2}^{x^{2} x \neq 2} is not continous at x = 2

Answered by sandy_suhendra last updated on 23/Jan/17

(i) f (2) = 2^{2} = 4

li \underset{x \to 2}{m} x^{2} = 2^{2} = 4

f (x) = x^{2} is continuos at x = 2

because f (2) = li \underset{x \to 2}{m} f (x)

(ii) f (2) = 0

li {\underset{x \to 2_{}}{m x}}^{2} = 2^{2} = 4

f (x) = x^{2} is not continuous at x = 2

because f (2) \neq li \underset{x \to 2}{m} f (x)

Commented by Tawakalitu ayo mi last updated on 23/Jan/17

God bless you sir .