Show that f(x)=fracx2+x-6x2-4, x neq 2 has a continuous extension to x | Basic Mathematics 2077

Basic Mathematics20775 marksNumerical: continuous extension of functionContinuous extension of functions

Show that $f(x)=\frac{x^2+x-6}{x^2-4}$ , $x \neq 2$ has a continuous extension to $x=2$ [5]

Show that $f(x)=\frac{x^2+x-6}{x^2-4}$, $x \neq 2$ has a continuous extension to $x=2$ [5]

Function: $f(x) = \dfrac{x^2 + x - 6}{x^2 - 4}$ , defined for $x \neq 2$ . - Target point for extension: $x = 2$ . Direct substitution: $f(2) = \frac{2^2 + 2 - 6}{2^2 - 4} = \frac{0}{0}$ This is indeterminate, so $f$ is not defined at $x = 2$ . We test whether the limit exists (a removable discon...

Function: $f(x) = \dfrac{x^2 + x - 6}{x^2 - 4}$, defined for $x \neq 2$. - Target point for extension: $x = 2$. Direct substitution: $$f(2) = \frac{2^2 + 2 - 6}{2^2 - 4} = \frac{0}{0}$$ This is indeterminate, so $f$ is not defined at $x = 2$. We test whether the limit exists (a removable discon...

Show that f(x)=fracx2+x-6x2-4, x neq 2 has a continuous extension to x=2