How do you find the domain of the following functions #f(x)= ln(xx^2)#?
The domain is the open interval
By signing up, you agree to our Terms of Service and Privacy Policy
To find the domain of the function ( f(x) = \ln(xx^2) ), you need to determine the values of ( x ) for which the function is defined. Since the natural logarithm function ( \ln(x) ) is defined only for positive values of ( x ), we need to ensure that ( x  x^2 > 0 ).

Solve the inequality ( x  x^2 > 0 ) for ( x ): ( x  x^2 > 0 ) ( x(1  x) > 0 )

Find the critical points by setting each factor equal to zero: ( x = 0 ) and ( 1  x = 0 ) Solving ( 1  x = 0 ) gives ( x = 1 ).

Create a sign chart to determine the intervals where ( x(1  x) > 0 ):
[ \begin{array}{cccc} \hline \text{Interval} & x & 1  x & x(1  x) > 0 \ \hline (\infty, 0) & \text{negative} & \text{positive} & \text{negative} \ (0, 1) & \text{positive} & \text{positive} & \text{positive} \ (1, \infty) & \text{positive} & \text{negative} & \text{negative} \ \hline \end{array} ]

Determine the domain: Since ( x(1  x) > 0 ) for ( x \in (0, 1) ), the domain of ( f(x) = \ln(xx^2) ) is ( \boxed{(0, 1)} ).
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
 How do you find the asymptotes for #r(x) = (1) / (x+ 1)^2#?
 How do you find the asymptotes for #f( x ) = tan(x)#?
 How do you find the asymptotes for #f(x) = (x^2  8)/(x+3)#?
 For #(x^2+1)/(2x^23x2)#, how do you find horizontal and vertical asymptotes?
 How do you find the inverse of #f(x) = (2x)/(x1)#?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7