Question

lim
x→0 f(x) where f(x) =(2|x|)/x if x does not equal 0, and 0 if x = 0. It's a piecewise function and I can't understand how to go about solving it. Thanks!

Answer 1

just use your normal limit rules but split the absolute value into the 2 cases where x is positive and x is negative you'll get the x's to cancel but be careful with the signs

Answer 2

ie. check whether the right hand limit equals the left hand limit