Question

Consider the function f(x) = {(sinx)/x, x cannot equal 0

{k, , x = 0
In order for f(x) to be continuous at x - 0, the value of k must be..

Answer 1

The continuity condition demands that the value of the function at x =0 equals the limi of the function as x ->0

As x -> 0, Limit of [sin (x) / x ] = 1.

Then, given that f(0) = k , k must be 1.

Answer: k must be 1.