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Let f(x) = \(\begin{cases} 1+\text x^2,\quad 0\leq\text x\leq 1\\ 2 - \text x,\quad \text x>1 \end{cases} \)

{ 1 + x2, 0 ≤ x ≤ 1, 2 - x, x >1

Show that \(\lim\limits_{\text x \to1} \) f(x) does not exist.

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f(x) = \(\begin{cases} 1+\text x^2,\quad 0\leq\text x\leq 1\\ 2 - \text x,\quad \text x>1 \end{cases} \)

{ 1 + x2, 0 ≤ x ≤ 1, 2 - x, x >1

Left Hand Limit(L.H.L.):

Right Hand Limit(R.H.L.):

Thus, \(\lim\limits_{\text x \to0} \) f(x) does not exist.

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