Question:
Find \(\lim_{x\rightarrow 1}\) f(x) where { x2 -1, x≤1 -x2-1, x>1
Find \(\lim_{x\rightarrow 1}\) f(x) where { x2 -1, x≤1 -x2-1, x>1
Updated On: Oct 23, 2023
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Solution and Explanation
The given function is
f(x) ={ x2 -1, x≤1 -x2-1, x>1
\(\lim_{x\rightarrow 1^-}\) f(x) =\(\lim_{x\rightarrow 1}\) [x2 -1] = 12 -1 =1-1 = 0
\(\lim_{x\rightarrow 1^+}\) f(x) = \(\lim_{x\rightarrow 1}\) [-x2 -1] = -12 -1 =-1-1 = -2
It is observed that \(\lim_{x\rightarrow 1^-}\) f(x) ≠\(\lim_{x\rightarrow 1^+}\) f(x).
Hence , \(\lim_{x\rightarrow 1}\) f(x) does not exist.
f(x) ={ x2 -1, x≤1 -x2-1, x>1
\(\lim_{x\rightarrow 1^-}\) f(x) =\(\lim_{x\rightarrow 1}\) [x2 -1] = 12 -1 =1-1 = 0
\(\lim_{x\rightarrow 1^+}\) f(x) = \(\lim_{x\rightarrow 1}\) [-x2 -1] = -12 -1 =-1-1 = -2
It is observed that \(\lim_{x\rightarrow 1^-}\) f(x) ≠\(\lim_{x\rightarrow 1^+}\) f(x).
Hence , \(\lim_{x\rightarrow 1}\) f(x) does not exist.
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