2º Lista de exercícios - Limites

Question 1

Observe o gráfico de f e marque as alternativas corretas.

Accepted Answer

$\displaystyle\lim_{x \to 2^+} f(x)=0$

Accepted Answer

$\displaystyle\lim_{x \to 0^+} f(x)=2$

Accepted Answer

$\displaystyle\lim_{x \to -2^+} f(x)=0$

Accepted Answer

$\displaystyle\lim_{x \to -2^-} f(x)=3$

Accepted Answer

$\displaystyle\lim_{x \to -2} f(x)= \nexists
$

Answer

$\displaystyle\lim_{x \to -2} f(x)=3$

Answer

$\displaystyle\lim_{x \to 2} f(x)= \nexists
$

Question 2

Seja f uma função tal que f(x) = 3x+2, x $ \in \mathbb{R}$. Se $\displaystyle\lim_{x \to 1} f(x) = 5$,$\\$ encontre um $\delta$ para $\epsilon$=0,01, tal que 0 < $\mid$x-1$\mid$ < $\delta$$\rightarrow$$\mid$f(x)-5$\mid$< 0,01.

Accepted Answer

0<$\delta$< $\frac{0,01}{3}$

Answer

0<$\delta$<0,01

Answer

0<$\delta$< $\frac{0,01}{5}$

Answer

0<$\delta$< $\frac{1}{5}$

Question 3

Dada f(x) = $\frac{\mid x \mid}{x}$. O que podemos afirmar sobre $\displaystyle\lim_{x \to 0} f(x)$?

Accepted Answer

$\displaystyle\lim_{x \to 0^-} f(x)=-1$

Accepted Answer

$\displaystyle\lim_{x \to 0^+} f(x)=1$

Accepted Answer

$\displaystyle\lim_{x \to 0} f(x)= \nexists$

Answer

$\displaystyle\lim_{x \to 0^+} f(x)=0$

Question 4

Encontre $\displaystyle\lim_{x \to 1} f(x)$, sabendo que: $$ f(x) = \left\{\begin{array}{rll} 3x-2 & \hbox{se} & x>1 \ 2 & \hbox{se} & x=0 \ 4x+1 & \hbox{se} & x<1
\end{array}\right.$$

Accepted Answer

$\displaystyle\lim_{x \to 1} f(x)= \nexists$

Answer

$\displaystyle\lim_{x \to 1} f(x)=1$

Answer

$\displaystyle\lim_{x \to 1} f(x)=5$

Answer

$\displaystyle\lim_{x \to 1} f(x)=2$

2º Lista de exercícios - Limites

Preguntas del test (4)

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