Question

alguém me ajuda nessa, se eu ver como responde essa talvez consiga fazer o resto ​

Answer 1

$\displaystyle \lim_{\text t \to \frac{1}{2}}\ \frac{\text t^3-5\text t^2+5^{4\text t}-\text{ln(2t) }}{2\text t}$

fazendo $\displaystyle \text t = \frac{1}{2}$ :

$\displaystyle \lim_{\text t \to \frac{1}{2}}\ \frac{\text t^3-5\text t^2+5^{4\text t}-\text{ln(2t) }}{2\text t} \\\\\\ \frac{\displaystyle \frac{1}{2^3}-5.\frac{1}{2^2}+5^{4\frac{1}{2}} - \text{ln}(2.\frac{1}{2}) }{\displaystyle 2.\frac{1}{2}}\\\\\\\ \frac{\displaystyle \frac{1}{8}-\frac{5}{4}+5^{\frac{4}{2}-\text{ln}(1)}}{\frac{2}{2}} \\\\\\ \frac{1}{8}-\frac{5}{4} + 25 - 0 \\\\\\\ \frac{1-10+200}{8} \\\\\ \boxed{\frac{191}{8}}$

Portanto, concluímos que  :

$\huge\boxed{\displaystyle \lim_{\text t \to \frac{1}{2}}\ \frac{\text t^3-5\text t^2+5^{4\text t}-\text{ln(2t) }}{2\text t} = \frac{191}{8}} \checkmark$