How do you evaluate (5-t) / | 5- t | as x approaches 5^-?

2 Answers

Hence t->5^- that means 5-t>0 hence abs(5-t)=5-t

and lim_(t->5^-) (5-t)/(abs(5-t))=lim_(t->5^-) (5-t)/(5-t)=1

May 25, 2016

The function is discontinuous at t = 5. The limit = +-1

Explanation:

#|5-t|=5-t, when t < 5 and t-5, when t > 5.

So, for #t < 5, (5-t)/|5-t|= (5-t)/(5-t)=1

and for any t >5, (5-t)/|5-t|= (5-t)/(t-5)=-1.

The answer is now clear, +-1.

and the graph for x = (5-t)/|5-t| reveals the fall, at t = 5.