Question

ДАЮ 20 БАЛЛОВ, РЕШИТЕ ПОЖАЛУЙСТА, ЛЮБЫЕ

Answer 1

1)
$lim_{x to infty} frac{5x^2+11x-3}{-x^2-2x+3} = lim_{x to infty} frac{ frac{5x^2}{x^2} + frac{11x}{x^2} - frac{3}{x^2} }{- frac{x^2}{x^2} - frac{2x}{x^2} + frac{3}{x^2} } = frac{5}{-1} =-5$

2)
$lim_{x to infty} frac{2x^3-2x^2}{x^4+x-3} = lim_{x to infty} frac{ frac{2x^3}{x^3} - frac{2x^2}{x^3} }{ frac{x^4}{x^3} + frac{x}{x^3} - frac{3}{x^3} } = lim_{x to infty} frac{2}{x} = frac{2}{infty}=0$

3)
$lim_{x to -2} frac{x+2}{x^2-x-6} = lim_{x to -2} frac{x+2}{(x+2)(x-3)} =lim_{x to -2} frac{1}{x-3} = frac{1}{-5} =-0.2$

4)
$lim_{x to 3} frac{9-x^2}{27-x^3} = lim_{x to 3} frac{(3-x)(3+x)}{(3-x)(x^2+3x+9)} = lim_{x to 3} frac{3+x}{x^2+3x+9} = frac{6}{27}= frac{2}{9}$

5)

6)
$lim_{x to 4} frac{x-4}{ sqrt{x+5} -3} = lim_{x to 4} frac{(x-4)(sqrt{x+5} +3)}{ (sqrt{x+5} -3)(sqrt{x+5} +3)} =\\ lim_{x to 4} frac{(x-4)(sqrt{x+5} +3)}{ x-4} = lim_{x to 4} (sqrt{x+5} +3)= 6$

7)
$lim_{x to 0} frac{ sqrt{1+x}-1 }{5x} = lim_{x to 0} frac{ (sqrt{1+x}-1)(sqrt{1+x}+1) }{5x(sqrt{1+x}+1)} =\\lim_{x to 0} frac{ x}{5x(sqrt{1+x}+1)} =lim_{x to 0} frac{ 1}{5(sqrt{1+x}+1)} = frac{1}{5*2} =0.1$

Answer 2

5 номер не смог

Answer 3

СПАСИБО БОЛЬШОЕ!