Question

Please show how f(x)=(2x+3)/(x-2) is continue in the interval ]2,infinity[

Answer 1

Answer:

See below

Step-by-step explanation:

A function is continuous within an interval if its first derivative exists
$\text{The first derivative of }\dfrac{2x+3}{x\:-\:2} = \dfrac{d}{dx}\left(\dfrac{2x+3}{x\:-\:2}\right) = -\dfrac{7}{\left(x-2\right)^2}$

Let's call this first derivative g(x)

g(x) is defined at all values of x except at x=2 since at this value the denominator becomes 0 and g(x) is not defined.

So the function has a discontinuity at x = 2

But in the interval (2, ∞ ) the function g(x)  always has a real value so f(x) is continuous in that interval