Use an appropriate formal definition to give a formal proof of each of the following.

(a) lim (x^{3}− 5x+6) = 2

x→1

(b) lim9-4x^{2 }_{= 6}

x→ −1.5 3+2x

(c) lim1_{= ∞}

x→ −3 (x+3)^{4}

(d) lim lnx = - ∞

x→0^{+}

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