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Let f(x) = \(\begin{cases} \cfrac{3\text x}{|\text x|+2\text x},\quad \text x\neq 0 \\ 0,\quad \text x=0 \end{cases} \)

{3x/(|x| + 2x), x ≠ 0, 0, x = 0,

Show that \(\lim\limits_{\text x \to0} \) f(x) does not exist.

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f(x) = \(\begin{cases} \cfrac{3\text x}{|\text x|+2\text x},\quad \text x\neq 0 \\ 0,\quad \text x=0 \end{cases} \)

{3x/(|x| + 2x), x ≠ 0, 0, x = 0

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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