Piece wise function?
Let f(x) = { x^2+1 if x does not equal 1
4 if x = 1
Which of the following statements is/are true?
I. lim f(x) exists
x–>1
II. f(1) exists
III. f is continuous at x = 1
Top 2 Answers
Favorite Answer
1.
The function g(x) = x^2 + 1 has value 2 when x = 1.
g(x) approaches 1 from above and from below as x approaches (but does not equal) 1.
Therefore lim(x -> 1) f(x) exists and is equal to 2.
2.
f(1) exists, and is defined as equal to 4.
3.
f is not continuous at x = 1 as f(1) is not equal to the limit described in answer 1 above.
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Your confusing me with someone who cares.
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