Question

1) lim x-> 3 x^2-5x+6/x^2-9 2) lim x-> oo 1-2x^2/x^2+4x 3) lim x-> oo 1-√1-x^2/x^2

Answer 1

$\lim_{x \to3} \frac{x^2-5x+6}{x^2-9} =[ \frac{0}{0} ]= \lim_{x \to3} \frac{(x-2)(x-3)}{(x+3)(x-3)} = \lim_{x \to3} \frac{x-2}{x+3}= \frac{3-2}{3+3} = \frac{1}{6}\\ \lim_{x \to \infty} \frac{1-2x^2}{x^2+4x} = \lim_{x \to \infty} \frac{x^2( \frac{1}{x^2} -2)}{x^2(1+ \frac{4}{x}) } = \lim_{x \to \infty} \frac{-2+ \frac{1}{x^2} }{1+ \frac{4}{x}} = \frac{-2+0}{1+0} =-2$

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