Question

If `lim_{x\to\4}(f(x))=0`, find the value of `lim_{x\to\4}(x*f(x))` ?

Answer 1

`lim_(xrarr4)(x*f(x)) = 0`

Explanation:

Using the product property of limits:

`lim_(xrarr4)(x*f(x)) = lim_(xrarr4)x * lim_(xrarr4)f(x)` if both limits on the right exist.

`lim_(xrarr4)x= 4` and `lim_(xrarr4)f(x) = 0`.

Therefore the limits do exist and

`lim_(xrarr4)(x*f(x)) = lim_(xrarr4)x * lim_(xrarr4)f(x) = 4 * 0 = 0`#