1.1) Calcule $\lim f\left(a_n\right)$ onde:

(a) $f\left( x \right) = 4x - 24$ e ${a_n} = \frac{{3n - 2}}{n}$;

(b) $f\left( x \right) = \ln x$ e ${a_n} = {e^4} + \frac{8}{{{n^2}}}$.

(c) $f\left( x \right) = 2{x^2} - 3x + 5$ e ${a_n} = \frac{1}{n}$.

 

1.2) Na figura seguinte está representado o gráfico de uma função real de variável real $f$.

Indique ou justifique que não existe:

(a) $\displaystyle\mathop {\lim }\limits_{x \to -4^+} f\left(x \right)$;	(b) $\displaystyle\mathop {\lim }\limits_{x \to -2^-} f\left(x \right)$;	(c) $\displaystyle\mathop {\lim }\limits_{x \to -2^+} f\left(x \right)$	(d) $\displaystyle\mathop {\lim }\limits_{x \to 2^-} f\left(x \right)$;
(e) $\displaystyle\mathop {\lim }\limits_{x \to 2^+} f\left(x \right)$;	(f) $\displaystyle\mathop {\lim }\limits_{x \to 2} f\left(x \right)$;	(g) $\displaystyle\mathop {\lim }\limits_{x \to 8^-} f\left(x \right)$.

 

 

1.3) Considere o gráfico da função real de variável real $f$ do exercício anterior. Calcule:

(a) $\lim f\left(-4+\frac{1}{n}\right)$;	(b) $\lim f\left(-2-\frac{2}{n^2}\right)$;	(c) $\lim f\left(-2+\frac{1}{2^n}\right)$;	(d) $\lim f\left(2-\frac{1}{n^2+1}\right)$;
(e) $\lim f\left(\frac{2n+3}{n+1}\right)$;	(f) $\lim f\left(8+\frac{1}{\sqrt{n}}\right)$;	(g) $\lim f\left(2+\frac{(-1)^n}{n}\right)$;