# How do you find #lim (1/t-1)/(t^2-2t+1)# as #t->1^+# using l'Hospital's Rule?

##### 1 Answer

Jul 21, 2017

Te limit does not exist

#### Explanation:

We seek:

# L = lim_(t rarr 1^+) (1/t-1)/(t^2-2t+1)#

From the graph it would appear that the limit does **not** exist:

graph{(1/x-1)/(x^2-2x+1) [-5, 5, -6, 6]}

As this is of an indeterminate form

# L = lim_(t rarr 1^+) (d/dt(1/t-1) )/( d/dt (t^2-2t+1) )#

# \ \ = lim_(t rarr 1^+) (-1/t^2 )/( 2t-2 )#

# \ \ rarr oo# , as predicted