How do you evaluate the limit #-(t-2)/(t^2-4)# as t approaches #2#?

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Answer 1 · 2016-10-06T17:28:50

#-1/4.#

Reqd. Limit#=lim_(trarr2)-(t-2)/(t^2-4)#

#=lim_(trarr2)-cancel((t-2))/{cancel((t-2))(t+2)}#

#=lim_(trarr2)-1/(t+2)#

#=-1/(2+2)#

#=-1/4.#

Answer 2 · 2016-10-06T17:31:48

#lim_(trarr2)(-(t-2)/(t^2-4))=color(green)(-1/4)#

If #t!=2#
then#(t-2)/(t^2-4)= (t-2)/((t-2)(t+2))=1/(t+2)#
and
#lim_(trarr2)(-(t-2)/(t^2-4)) = lim_(trarr2)(-1/(t+2))=-1/4#