Question

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

Answer 1

Answer:

$\lim_{x \to 2} \frac{x^{2} }{x^{2} +4} = \frac{1}{2} = f(C)$

The  function f(x) is continuous

Step-by-step explanation:

Explanation:-

Given that the function

                   $f(x) = \frac{x^{2} }{x^{2} +4}$

    put  x = c =2

                 $f(c) = f(2) = \frac{(2)^{2} }{(2)^{2} +4} = \frac{4}{8} = \frac{1}{2}$

              $\lim_{x \to 2} \frac{x^{2} }{x^{2} +4} = \frac{2^{2} }{2^{2} +4} = \frac{4}{4+4} = \frac{4}{8}$

              $\lim_{x \to 2} \frac{x^{2} }{x^{2} +4} = \frac{1}{2}$

$\lim_{x \to 2} \frac{x^{2} }{x^{2} +4} = \frac{1}{2} = f(C)$

      Given function f(x) is continuous