Question

Se lim f(x) -8/ x-1 =10 entao lim f(x) x-->1 é ?
x-->1

lim senx²/x
x-->0

lim sen (x -1) / x² +x -2
x-->1

Answer 1

limite fundamental
$\boxed{\boxed{ \lim_{x \to 0} \frac{sen(x)}{x}=1 }}$

reescrevendo

$\lim_{x \to 0} \frac{sen^2(x)}{x} = \frac{sen(x)*sen(x)}{x} = \frac{sen(x)}{x}*sen(x) = 1*sen(x)\\\\\\\lim_{x \to 0} \frac{sen^2(x)}{x} =sen(x) = sen(0)$
::::::::::::::::::::::::::::::::::::::::::::::::::::::::

$\lim_{x \to 1} \frac{sen(x-1)}{x^2+x-2} = \frac{sen(x-1)}{(x-1)*(x+2)} = \frac{sen(x-1)}{(x-1)}* \frac{1}{(x-2)} = 1* \frac{1}{1-2} = - 1$