Answer to Question #310858 in Real Analysis for Nikhil rawat

Question

Check whether the function f given by

f(x)=1/(2x-4)^2 ∀x∈]-2,2[

Is continuous in the interaval ]-2,2] but not bounded in the interval (-2,2)

Answer 1

The function is continuous since it is rational function with the denominator non-zero on (-2,2). It is not bounded since $f(2-\frac{1}{2n})=n^2\to +\infty, n\to\infty$