x → 4 lim x 2 − 8 x + 16 x − 4 = x → 4 lim ( x − 4 ) 2 x − 4 = x → 4 lim x − 4 1 x → 4 − lim x − 4 1 = 0 − 1 = − ∞ x → 4 + lim x − 4 1 = 0 + 1 = ∞
The limit lim x → 4 x 2 − 8 x + 16 x − 4 does not exist because the left-hand limit approaches -∞ while the right-hand limit approaches +∞. Thus, the limits diverge, confirming that the limit overall is undefined. Therefore, since both one-sided limits do not agree, the limit does not exist.
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