Question

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

Answer 1

`\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