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

Olá
Resolvendo temos:
$\lim_{x \to } _{1} (2 x^{4}+2 x^{3}+ x-3) \\ \\ x=1 \\ (2 (1^{4} )+2( 1^{3} )+1-3 \\ 2+2+1-3 \\ =2$

b)

$\lim_{x \to \ 5 \frac{ x^{2} -25}{x-5} = \frac{ x^{2} - 5^{2} }{x-5} = \frac{(x-5)(x+5)}{x-5}$

cortamos (x-5)

$(x+5)-------->x=5 5+5=10....resposta.$

c)

$\lim_{x \to \ o \frac{ x^{4}+ x^{3}- x^{2} +1 }{ x^{2} +1}$

x=0
 
         $\frac{ 0^{4}+ 0^{3}- 0^{2} +1 }{ 0^{2}+1 }= \frac{1}{1} =1$