Determine \( \int y d x \) in each of the following cases: \( \quad y=2 \sec ^{2}\left(\frac{\pi}{3} x\right) \tan \left(\frac{\pi}{3} x\right) \)

6. If \( f(x)=\left\{\begin{array}{ll}x+2, & x \leq-1 \\ c+2 & x>-1\end{array}\right. \) find "c" so that \( \lim _{x \rightarrow-1} f(x) \) exists. 7. Evaluate \( \lim \frac{\operatorname{Sin} x^{0}}{} \)

For the function \( f(x)=5 x+1 \), find \( (a) f(x+h),(b) f(x+h)-f(x) \), and \( (c) \frac{f(x+h)-f(x)}{h} \)

Funcion de transferencia \( \begin{array}{ll}m x^{\prime \prime}+b x^{\prime}+k x=0 & x(0)=1 \\ m=1 k g \quad b=5 \quad k=4 & v_{0}=0\end{array} \)

31. \( \int_{0}^{2}(3 x+4) d x \)

29. \( \int_{0}^{4} x d x \)