Question

3 multiple choice 2 points
what is the maximum of the function ( f(x)=xsqrt{5 - x} )?
( \frac{5sqrt{5}}{3} )
( \frac{10sqrt{15}}{9} )
5
( \frac{10}{3} )
no maximum
4 multiple choice 2 points
what is the domain of ( f(x)=\frac{1 - e^{-x}}{x} )?
( (-infty,infty) )
( (-infty,0)cup(0,infty) )
( (0,infty) )
( 0,infty) )
( (-infty,0 )

Explanation:

Step1: Find the domain of \(f(x)\)

For the function \(f(x)=\frac{1 - e^{-x}}{x}\), the denominator \(x
eq0\). Since \(e^{-x}\) is defined for all real \(x\), the domain is all real numbers except \(x = 0\).

Answer:

\((-\infty,0)\cup(0,\infty)\)