Question

The function `f(x) = [x^2 + x] / [x]` is defined and continuous for all x except x = 0. What value of x must be assigned to f(x) for x = 0 in order that the function be continuous at x = 0?

Answer 1

In order for `f` to be continuous at `0`, the definition of continuous says we must have:

`lim_(xrarr0) f(x) = f(0)`

This question asks what number must you put on the right (as `f(0)`) in order for the equation to be true.

To answer this, you need to find

`lim_(xrarr0) (x^2+x)/x`