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?

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?

smeachtaczm · Accepted Answer

In order for f to be continuous at 0, the definition of continuous says we must have:            lim              x        →        0                    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              x        →        0                                      x          2                +        x            x

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?

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