How do you find #\lim _ { x \rightarrow 4} \root [ 3] { \frac { x } { - 7x + 1} }#?
1 Answer
Jan 25, 2017
Can't you just plug it in?
#color(blue)(lim_(x->4) (x/(-7x + 1))^"1/3")#
#= (4/(-7*4 + 1))^"1/3"#
#= (-4/(27))^"1/3"#
#= ((-2^2)/(27))^"1/3"#
#= ((-1)^"1/3" 2^"2/3")/(3)#
#= -(2^"2/3")/(3)#
#~~ color(blue)(-0.5291)#
We can check that here:
graph{(x/(-7x + 1))^(1/3) [-0.91, 6.885, -2.525, 1.37]}
