What is the continuity of #f(t) = 3 - sqrt(9-t^2)#? Calculus Limits Definition of Continuity at a Point 1 Answer Jim H May 1, 2015 #f(t) = 3 - sqrt(9-t^2)# has domain #[-3,3]# For #a# in #(-3,3)#, #lim_(trarra) f(t) = f(a)# because #lim_(trarra)(3 - sqrt(9-t^2)) = 3-lim_(trarra) sqrt(9-t^2)# #= 3-sqrt(lim_(trarra) (9-t^2)) = 3-sqrt(9-lim_(trarra) t^2))# #=3-sqrt(9-a^2) = f(a)# So #f# is continuous on #(-3,3)#. Similar reasoning will show that #lim_(trarr-3^+) f(t) = f(-3)# and #lim_(trarr3^-) f(t) = f(3)# So #f# is continuous on #[-3,3]#. Answer link Related questions What are the three conditions for continuity at a point? What is continuity at a point? What is the definition of continuity at a point? What does continuous at a point mean? What makes a function continuous at a point? How do you find the points of continuity and the points of discontinuity for a function? What does continuity mean? How do you use continuity to evaluate the limit #arctan(x^2-4)/(3x^2-6x)#? How do you find the points of continuity of a function? How do you find the continuity of a function on a closed interval? See all questions in Definition of Continuity at a Point Impact of this question 4726 views around the world You can reuse this answer Creative Commons License