Question

Сделайте с пошаговым решением, пожалуйста.

Answer 1

1.
$lim_{xto 1} frac{2x^2 +3x - 1}{x^4 - 1} = infty$
$lim_{xto 1} frac{2x^2 +3x - 1}{x^4 - 1} = (lim_{xto 1} 2x^2 +3x - 1)*lim_{xto 1}(frac{1}{x^4 - 1}) = 4*infty = infty$
2.
$lim_{x to infty} frac{2x^2 + 7x + 3}{5x^2 - 3x + 4} = lim_{x to infty} frac{x^2(2 + frac{7}{x} + frac{3}{x^2}) }{x^2(5 - frac{3}{x} + frac{4}{x^2}) } = lim_{x to infty} frac{(2 + frac{7}{x} + frac{3}{x^2}) }{(5 - frac{3}{x} + frac{4}{x^2}) } = frac{2}{5}$
3.
$lim_{x to infty} frac{x^7 + 5x^2 - 4x}{3x^2 +11x - 7} = lim_{x to infty} frac{x^2(x^5 + 5 - 4/x)}{x^2(3 +11/x - 7/x^2)} = lim_{x to infty} frac{(x^5 + 5 - 4/x)}{(3 +11/x - 7/x^2)}$
$lim_{x to infty} frac{(x^5 + 5 - 4/x)}{(3 +11/x - 7/x^2)} = lim_{x to infty} frac{infty + 5 - 0}{3} = infty$