Answer to Question #301415 in Calculus for Jimjim

Question

1.if f(x)=x^2-1/1+x^2,find f(-1),f(2),f(1/2),f(tan x).

2.graph the surface area of a cube as a function of the volume of a cube.

Answer 1

1) $f(x)=\frac{x^2-1}{1+x^2}$

$f(-1)=\frac{1-1}{1+1}=0$

$f(2)=\frac{4-1}{1+4}=\frac{3}{4}$

$f(\frac{1}{2})=\frac{\frac{1}{4}-1}{1+\frac{1}{4}}=-\frac{3}{5}$

$f(\tan x)=\frac{\tan^2 x-1}{\tan^2x+1}=\sin^2x-\cos^2x=1-2\cos^2x$

2) $V=a^3\to a=V^\frac{1}{3}$

$S=6a^2=6V^\frac{2}{3}$