How do you prove that the function f(x) = x^2 -3x +5 is continuous at a =2?

Zachariah Norris 2022-09-15 Answered
How do you prove that the function f ( x ) = x 2 - 3 x + 5 is continuous at a =2?
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Answers (1)

ti1k1le2l
Answered 2022-09-16 Author has 6 answers
Any polynomial function is continuous everywhere, but let's prove this particular example using the limit definition of continuity...
A function f(x) is continuous at a point a if both f(a) and lim x a f ( x ) are defined and equal.
In our example:
f ( 2 ) = 2 2 - 3 ( 2 ) + 5 = 4 - 6 + 5 = 3
= 2 2 + 4 h + h 2 - 3 ( 2 ) - 3 h + 5
= 2 2 + 4 h + h 2 - 3 ( 2 ) - 3 h + 5
= 4 - 6 + 5 + h + h 2
= 3 + h + h 2 3 as h 0
So lim x 2 f ( x ) = lim h 0 f ( 2 + h ) = 3 = f ( 2 )
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