$$\lim_{x \to \infty}\left(\frac{x^{2} \left(7^{\sin{\left(x \right)}} - 1\right) \log{\left(5 \right)}}{\log{\left(\tan{\left(3 x \right)} + 1 \right)}}\right)$$
$$\lim_{x \to 0^-}\left(\frac{x^{2} \left(7^{\sin{\left(x \right)}} - 1\right) \log{\left(5 \right)}}{\log{\left(\tan{\left(3 x \right)} + 1 \right)}}\right) = 0$$
Más detalles con x→0 a la izquierda$$\lim_{x \to 0^+}\left(\frac{x^{2} \left(7^{\sin{\left(x \right)}} - 1\right) \log{\left(5 \right)}}{\log{\left(\tan{\left(3 x \right)} + 1 \right)}}\right) = 0$$
Más detalles con x→0 a la derecha$$\lim_{x \to 1^-}\left(\frac{x^{2} \left(7^{\sin{\left(x \right)}} - 1\right) \log{\left(5 \right)}}{\log{\left(\tan{\left(3 x \right)} + 1 \right)}}\right) = \frac{- \log{\left(5 \right)} + 7^{\sin{\left(1 \right)}} \log{\left(5 \right)}}{\log{\left(\tan{\left(3 \right)} + 1 \right)}}$$
Más detalles con x→1 a la izquierda$$\lim_{x \to 1^+}\left(\frac{x^{2} \left(7^{\sin{\left(x \right)}} - 1\right) \log{\left(5 \right)}}{\log{\left(\tan{\left(3 x \right)} + 1 \right)}}\right) = \frac{- \log{\left(5 \right)} + 7^{\sin{\left(1 \right)}} \log{\left(5 \right)}}{\log{\left(\tan{\left(3 \right)} + 1 \right)}}$$
Más detalles con x→1 a la derecha$$\lim_{x \to -\infty}\left(\frac{x^{2} \left(7^{\sin{\left(x \right)}} - 1\right) \log{\left(5 \right)}}{\log{\left(\tan{\left(3 x \right)} + 1 \right)}}\right)$$
Más detalles con x→-oo