Question

Para que a função f definida por
seja contínua em x = 1, devemos ter:




a.
k = 0


b.
k = -1


c.
k = -2


d.
k = 2


e.
k = 1

Answer 1

$\displaystyle \underline{\text{Fun{\c c}{\~a}o cont{\'i}nua}}: \\\\ \lim_{\text x\to \text a}\text{f(x)} = \text{f(a)}$

Temos :

$\displaystyle \text{f(x)}=\left \{ {{\displaystyle \frac{ 3\text x^2-4\text x+1}{\text x-1}\ \ .\ \text{se x}\neq1\ \\}\ \atop {\text x-\text k \ ; \ \ \text{se x}=1}} \right.$

$\displaystyle \text x = 1 \to \text{f(1) = 1 - k } \\\\\\ \lim_{\text x\to 1}(\frac{3\text x^2-4\text x+1}{\text x-1 }) =1-\text k \\\\\\\ \lim_{\text x \to 1}\frac{(3\text x-1)(\text x-1)}{\text x-1} =1-\text k \\\\\\ \lim_{\text x\to 1}3\text x-1 = 1-\text k \\\\ 3-1 = 1-\text k \\\\ \text k = 1+1-3 \\\\\ \huge\boxed{\text k = -1\ }\checkmark$

Letra b