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##