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

1 Answer
Dec 13, 2017

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#