Question

Calcule
a) $\lim_{x \to \01} ( 2x^{4} + 2x^{3} + x - 3 )$

b) $\lim_{x \to \05} \frac{x^{2} - 25}{x-5}$

c) $\lim_{x \to \00} \frac{ x^{4}+ x^{3} - x^{2} + 1 }{ x^{2} +1}$

Answer 1

a)
$\lim_{x \to 1} 2x^{4} + 2x^{3} + x - 3 = \\ = 2. 1^{4} + 2. 1^{3} + 1 - 3 = 2 + 2 - 2 = 2$
b)
$\lim_{x \to 5} \frac{ x^{2} - 25}{x - 5} = \lim_{x \to 5} \frac{(x - 5)(x + 5)}{x - 5} = \\ = \lim_{x \to 5} x + 5 = 5 + 5 = 10$
c)
$\lim_{x \to 0} \frac{ x^{4} + x^{3} - x^{2} +1}{ x^{2} + 1} = \\ \frac{ 0^{4} + 0^{3} - 0^{2} + 1}{ 0^{2} +1 } = \\ \frac{1}{1} = 1$