T3 Continuidad de Funciones
Encuentre los valores de las constantes c y k que hacen que la función sea continua en todo punto.
$$1) f(x) = \left\{ \begin{array}{ll} kx-1 & \mathrm{si\ } x \leq 2 \\ kx^2 & \mathrm{si\ } x > 2 \end{array} \right. $$
$$2) f(x) = \left\{ \begin{array}{ll} \:\:\:\:x & \mathrm{si\ } x \leq 1 \\ cx+k & \mathrm{si\ } 1 < x < 4\\ -2x & \mathrm{si\ } x \geq 4 \end{array} \right. $$
$$3) f(x) = \left\{ \begin{array}{ll} x+2c & \mathrm{si\ } x < -2 \\ 3cx+k & \mathrm{si\ } -2 \leq x \leq 1 \\ 3x-2k & \mathrm{si\ } x > 1 \end{array} \right. $$
$$4) f(x) = \left\{ \begin{array}{ll} 2x+1 & \mathrm{si\ } x\leq 1 \\ \:\:\:k & \mathrm{si\ } x > 1 \end{array} \right. $$
$$5) f(x) = \left\{ \begin{array}{ll} x^2+kx & \mathrm{si\ } x\leq 2 \\ k-x^2 & \mathrm{si\ } x > 2 \end{array} \right. $$
$$6) g(x) = \left\{ \begin{array}{ll} x+1 & \mathrm{si\ } x\leq 2 \\ 3-kx^2 & \mathrm{si\ } x > 2 \end{array} \right. $$
$$7) f(x) = \left\{ \begin{array}{ll} e^{kx} & \mathrm{si\ } x\leq 0 \\ x+2k & \mathrm{si\ } x > 0 \end{array} \right. $$
$$8) f(x) = \left\{ \begin{array}{ll} x^2+2x+1 & \mathrm{si\ } x < 0 \\ \:\:kx+c & \mathrm{si\ } 0 \leq x < 1\\ \:\:\:\:\:2 & \mathrm{si\ } x \geq 1 \end{array} \right. $$
$$7) f(x) = \left\{ \begin{array}{ll} 3x+6c & \mathrm{si\ } x < -3 \\ 3cx-7k & \mathrm{si\ } -3 \leq x \leq 3\\ x-12k & \mathrm{si\ } x > 3 \end{array} \right. $$
$$8) f(x) = \left\{ \begin{array}{ll} x^2 & \mathrm{si\ } x \leq -2 \\ cx+k & \mathrm{si\ } -2 < x < 2\\ 2x-5 & \mathrm{si\ } x \geq 2 \end{array} \right. $$
$$8) f(x) = \left\{ \begin{array}{ll} x^2 & \mathrm{si\ } x \leq -2 \\ cx+k & \mathrm{si\ } -2 < x < 2\\ 2x-5 & \mathrm{si\ } x \geq 2 \end{array} \right. $$
$$9) f(x) = \left\{ \begin{array}{ll} 2x+1 & \mathrm{si\ } x \leq 3 \\ cx+k & \mathrm{si\ } 3 < x < 5\\ x^2+2 & \mathrm{si\ } x \geq 5 \end{array} \right. $$
$$10) f(x) = \left\{ \begin{array}{ll} 3x+6c & \mathrm{si\ } x \leq -3 \\ 3cx-7k & \mathrm{si\ } -3 < x < 3\\ x-12k & \mathrm{si\ } x \geq 3 \end{array} \right. $$
$$11) f(x) = \left\{ \begin{array}{ll} \frac{x^4-1}{x-1} & \mathrm{si\ } x \neq 1 \\ \:\:\:k & \mathrm{si\ } x = 1 \end{array} \right. $$
$$12) f(x) = \left\{ \begin{array}{ll} \frac{1}{x^2}+k & \mathrm{si\ } x \leq -1 \\ 3x^2+4 & \mathrm{si\ } -1 < x < 1\\ -x^3+8 & \mathrm{si\ } x \geq 1 \end{array} \right. $$
$$13) f(x) = \left\{ \begin{array}{ll} x^2+2x+1 & \mathrm{si\ } x < 0 \\ \:\:kx+c & \mathrm{si\ } 0 \leq x < 1\\ \:\:\:\:\:2 & \mathrm{si\ } x \geq 1 \end{array} \right. $$
