Find \( f^{\prime}(x) \) \( f(x)=\frac{4 x-9}{7 x+4} \) \( f^{\prime}(x)=\square \)

\begin{tabular}{l} 4.3 - Riemann Sums \& The Definite Integral as Area \\ For each problem, approximate the area under the given function and above the \( x \)-axis on the given \\ interval using the specified number of rectangles/trapezoids. You may use your calculator. \\ 1.) \( f(x)=x^{2}-3 x+4,[1,4], n=6 \) \\ \begin{tabular}{|l|}\hline a) Left Rectangles \\ b) Right Rectangles \\ \hline c) Midpoint Rectangles \\ \hline d) Trapezoids \\ \hline\end{tabular} \\ \hline\end{tabular}

34. En cada uno de los siguientes casos, halle el valor de la constante \( A \) qu hace la función dada \( f(x) \) continua para todo \( x \). a) \( f(x)=\left\{\begin{array}{ll}2 x+3 & \text { si } x<1 \\ A x-1 & \text { si } x \geq 1\end{array}\right. \) b) \( f(x)=\left\{\begin{array}{ll}\frac{x^{2}-1}{x+1} & \text { si } x<-1 \\ A x^{2}+x-3 & \text { si } x \geq-1\end{array}\right. \)

(5) \( \int_{1}^{2} \frac{\sqrt{t^{2}-1}}{t^{3}} d t \)

\( \sum _ { i = 1 } ^ { 5 } \frac { 1 } { n ^ { 3 } } ( i - 1 ) ^ { 2 } \)

\( \sum _ { i = 1 } \frac { 1 } { n ^ { 3 } } ( i - 1 ) ^ { 2 } \)