Show that x²/√x²+4 is continuous at x=2

Question

asked Sep 21, 2022 151k views

1 Answer

Gunay Abdullayeva · Answer 1 · 2022-09-27T04:12:56+0000

Answer:

$\lim_(x \to 2) (x^(2) )/(x^(2) +4) = (1)/(2) = f(C)$

The function f(x) is continuous

Explanation:

Explanation:-

Given that the function

f(x) = (x^(2) )/(x^(2) +4)

put x = c =2

f(c) = f(2) = ((2)^(2) )/((2)^(2) +4) = (4)/(8) = (1)/(2)

$\lim_(x \to 2) (x^(2) )/(x^(2) +4) = (2^(2) )/(2^(2) +4) = (4)/(4+4) = (4)/(8)$

$\lim_(x \to 2) (x^(2) )/(x^(2) +4) = (1)/(2)$

$\lim_(x \to 2) (x^(2) )/(x^(2) +4) = (1)/(2) = f(C)$

Given function f(x) is continuous