What is the continuity of f(t) = 3 - sqrt(9-t^2)

Payton George 2022-10-12 Answered
What is the continuity of f ( t ) = 3 - 9 - t 2
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Answers (1)

Warkallent8
Answered 2022-10-13 Author has 16 answers
f ( t ) = 3 - 9 - t 2 has domain [ - 3 , 3 ]
For a in ( - 3 , 3 ) , lim t a f ( t ) = f ( a ) because
lim t a ( 3 - 9 - t 2 ) = 3 - lim t a 9 - t 2
= 3 - lim t a ( 9 - t 2 ) = 3 - 9 - lim t a t 2 )
= 3 - 9 - a 2 = f ( a )
So f is continuous on (−3,3).
Similar reasoning will show that
lim t - 3 + f ( t ) = f ( - 3 ) and
lim t 3 - f ( t ) = f ( 3 )
So f is continuous on [−3,3].
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