For each problem, approximate the area under the given function and above the \( x \)-axis on the give interval using the specified number of rectangles/trapezoids. You may use your calculator. 1.) \( f(x)=x^{2}-3 x+4,[1,4], n=6 \) a) Left Rectangles b) Right Rectangles c) Midpoint Rectangles d) Trapezoids

Use the quotient rule to find the derivative of the given function. \( f(t)=\frac{7 t^{2}-9 t}{9 t+5} \)

\( f ( x ) = \sqrt { \frac { x } { r - x ^ { r } } } \)

Find the derivative of the function \( f(x)=-\frac{x^{3}}{x-1} \)

Osrucuims fuzrarenui inmerpan: \( \int_{1}^{4} \sqrt{7 x-3} d x \)

The area bounded by the curve \( y=f(x) \) where \( y=n-\frac{n^{2}}{4}, x=\frac{n}{2} \) and \( X \)-axis equals....... square unit. \( \begin{array}{llll}\text { (a) } \frac{7}{3} & \text { (b) } \frac{3}{4} & \text { (c) } \frac{4}{3} & \text { (d) } \frac{3}{7}\end{array} \)