Describe the process of sketching a slope field for the differential equation \( y' = x + y \).

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

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. \( \begin{array}{llll}\text { (a) } \frac{7}{3} & \text { (b) } \frac{3}{4} & \text { (c) } \frac{4}{3} & \text { (d) } \frac{3}{7}\end{array} \)

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

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

3. Find the value of \( \lim _{x \rightarrow 0} \frac{x^{2}+3 x}{x} \) if it exists.