\( \int _ { 0 } ^ { \infty } \int _ { 0 } ^ { \infty } \frac { e ^ { - y } } { y } d y d x \)

\( \int \frac { x \ln x - x } { \ln ^ { 3 } x } \)

Given the functions \( f(x) = x^{\frac{1}{3}} \) and \( g(x) = x^{3} \), show that they are inverses by calculating their compositions \( f(g(x)) \) and \( g(f(x)) \).

19. If \( f(x)=\frac{1}{x} \) and \( g(x)=6-5 x \) then \( (f \circ g)(0) \) is? \( A, \frac{1}{6} \quad B, \frac{5}{6} \) 20. What is the solution set of \( 1-\frac{1}{\frac{x}{1-\frac{1}{x^{2}}}}=3 x^{2}-\frac{x}{1+\frac{1}{x}} \) \( \begin{array}{ll}\text { A. }\left\{-1, \frac{1}{3}\right\} & \text { C, }\left\{3,-\frac{1}{3}\right\} \\ \text { 21. Let } f(x)=x-x^{2} \& g(x)=\frac{1}{x} \text {, then what is } g\left(f\left(\frac{1}{x}\right)\right) \text { is equals to }\end{array} \)

seconds, is given by \( a(t)=t+1 \). Given that \( s=0 \) and \( v=8 \) when \( t=0 \), find formula for: (a) The velocity \( v \) (b) The displacement

The rate at which an object changes temperature, \( \frac{d T}{d t} \) is proportional to the difference between its temperature, \( T \) and the temperature of the surrounding medium, \( T_{s} \) \( \frac{d T}{d t}=k\left(T_{s}-T\right) \) (a) Solve the differential equation for \( T(t) \)