(iv) \( L\left(\frac{\partial^{2} y}{\partial x^{2}}\right)= \) (a) \( \frac{d^{2} \bar{y}}{d x^{2}} \) (b) 0 (c) 1 (d) -1 (v) \( \int_{0}^{\infty} \frac{\operatorname{Sin} t}{t} \cdot d t= \) (a) 0 (b) \( \pi / 4 \) (c) \( \pi / 2 \) (d) \( \pi \) (vi) \( L^{-1}\left\{\tan \frac{1}{p}\right\}= \) (a) \( \tan t \)

Determine the area between the curves \( y = x^2 \) and \( y = 4 - x^2 \) for the interval where they intersect.

A car's velocity is given by the function \( v(t) = 5t^2 + 3 \). Calculate the distance traveled by the car from time \( t = 0 \) to \( t = 4 \).

\( \lim ( 2 + \frac { 2 } { n } ) ^ { m } \)

\( F ^ { \prime } ( x ) = \lim _ { h \rightarrow 0 } \frac { \log _ { a } ( x + h ) - \log _ { a } ( x ) } { h } \)

A car's velocity is given by the function \( v(t) = 5t^2 + 3 \). Calculate the distance traveled by the car from time \( t = 0 \) to \( t = 4 \).