T2 Continuidad de Funciones
Determine si la función es continua en todo punto de su dominio, de no serlo indique los puntos en los que es discontinua.
$$ 1) f(x) = \left\{ \begin{array}{ll} \frac{x^2+x-6}{x+3} & \mathrm{si\ } x \neq -3 \\ \quad 1 & \mathrm{si\ } x = -3 \end{array} \right. $$
$$ 2) f(x) = \left\{ \begin{array}{ll} \frac{x^2-3x-4}{x-4} & \mathrm{si\ } x \neq 4 \\ \quad 2 & \mathrm{si\ } x = 4 \end{array} \right. $$
$$ 3) f(x) = \left\{ \begin{array}{ll} \frac{5}{x-4} & \mathrm{si\ } x \neq 4 \\ \:\:2 & \mathrm{si\ } x = 4 \end{array} \right. $$
$$ 4) f(x) = \left\{ \begin{array}{ll} \frac{1}{x+2} & \mathrm{si\ } x \neq -2 \\ \:\:0 & \mathrm{si\ } x = 2 \end{array} \right. $$
$$ 5) f(x) = \left\{ \begin{array}{ll} -1 & \mathrm{si\ } x < 0 \\ \:\:\: 0 & \mathrm{si\ } x = 0 \\ \sqrt{x} & \mathrm{si\ } x > 0 \end{array} \right. $$
$$ 6) f(x) = \left\{ \begin{array}{ll} x-1 & \mathrm{si\ } x < 1 \\ \:\:\:\: 1 & \mathrm{si\ } x = 1 \\ 1-x & \mathrm{si\ } x > 1 \end{array} \right. $$
$$ 7) g(t) = \left\{ \begin{array}{ll} t^2-4 & \mathrm{si\ } t < 2 \\ \:\:\: 4 & \mathrm{si\ } t = 2 \\ 4-t^2 & \mathrm{si\ } t > 2 \end{array} \right. $$
$$ 8) H(x) = \left\{ \begin{array}{ll} 6+x & \mathrm{si\ } \quad\: x \leq -2 \\ 2-x & \mathrm{si\ } -2 < x \leq 2\\ 2x-1 & \mathrm{si\ } \quad\: x > 2 \end{array} \right. $$
$$ 9) g(x) = \left\{ \begin{array}{ll} \frac{\left|x\right|}{x} & \mathrm{si\ } x\neq 0 \\ \:1 & \mathrm{si\ } x = 0 \end{array} \right. $$
$$ 10) f(x) = \left\{ \begin{array}{ll} 3x-1 & \mathrm{si\ } x < 2 \\ 4-x^2 & \mathrm{si\ } x \geq 2 \end{array} \right. $$
$$ 11) f(x) = \left\{ \begin{array}{ll} (x+2)^2 & \mathrm{si\ } x \leq 0 \\ x^2+2 & \mathrm{si\ } x > 0 \end{array} \right. $$
$$ 12) f(x) = \left\{ \begin{array}{ll} \frac{1}{x+1} & \mathrm{si\ } x \leq 1 \\ \frac{1}{3-x} & \mathrm{si\ } x > 1 \end{array} \right. $$
$$ 13) f(x) = \left\{ \begin{array}{ll} \:\frac{1}{x} & \mathrm{si\ } x < 3 \\ \frac{2}{9-x} & \mathrm{si\ } x \geq 3 \end{array} \right. $$
$$ 14) f(x) = \left\{ \begin{array}{ll} \frac{1}{x} & \mathrm{si\ } x < 3 \\ \frac{2}{9-x} & \mathrm{si\ } x \geq 3 \end{array} \right. $$
$$ 15) f(x) = \left\{ \begin{array}{ll} x+\sqrt[3]{x} & \mathrm{si\ } x < 0 \\ x-\sqrt{x} & \mathrm{si\ } x \geq 0 \end{array} \right. $$
$$ 16) h(x) = \left\{ \begin{array}{ll} 2x-\sqrt[3]{x} & \mathrm{si\ } x < 1 \\ x\sqrt{x} & \mathrm{si\ } x \geq 1 \end{array} \right. $$
$$ 17) f(x) = \left\{ \begin{array}{ll} 2x^2-1 & \mathrm{si\ } x < 0 \\ \frac{x-2}{2} & \mathrm{si\ } x \geq 0 \end{array} \right. $$
$$ 18) f(x) = \left\{ \begin{array}{ll} 3x-2 & \mathrm{si\ } x < 2 \\ 5 & \mathrm{si\ } x = 2\\ 3-x & \mathrm{si\ } x > 2 \end{array} \right. $$
$$ 19) f(x) = \left\{ \begin{array}{ll} \frac{x^2-5x+6}{x-3} & \mathrm{si\ } x \neq 3 \\ \:\:\:\:1 & \mathrm{si\ } x = 3 \end{array} \right. $$
$$ 20) f(x) = \left\{ \begin{array}{ll} x+1 & \mathrm{si\ } x < 3 \\ x^2 & \mathrm{si\ } 3 \leq x < 4 \\ \:\:\:0 & \mathrm{si\ } x \geq 4 \end{array} \right. $$ $$ 19) f(x) = \left\{ \begin{array}{ll} (x-1)+cos(x-1) & \mathrm{si\ } x \leq 1 \\ \qquad \frac{sen(x-1)}{x-1} & \mathrm{si\ } x > 1 \end{array} \right. $$
$$ 21) f(x) = \left\{ \begin{array}{ll} 2^x & \mathrm{si\ } x < 2 \\ \:4 & \mathrm{si\ } x \geq 2 \end{array} \right. $$ $$ 21) f(x) = \left\{ \begin{array}{ll} \qquad e^x & \mathrm{si\ } x \leq -1 \\ \left|x^2-x-2\right| & \mathrm{si\ } x > -1 \end{array} \right. $$
