Conceptual Doubt!! Differentiatuioin

yup Y=-Z because if u consider cancelling the √x² then u have to take it as lxl so it will be Y=-Z

This was how i did for Y, pl. spot the mistake .......

let t = 1/x ----> 0

Y = (tant/t)/(√8 + 7p + 1)

Y = 1/2√2 ................. wer did i miss out the minus SIgn??

Y = \lim_{x->infinity}x*[tan(1/x)/(1/x)]/\sqrt{8x^2+7x+1}
Y = \lim_{x->infinity}x/\sqrt{8x^2+7x+1} = \lim_{x-> infinity}x/\left|x \right|\sqrt{8+7/x+1/x^2}

if.x->-infinity.. then..x/\left|x \right| = -1..

so it is Y=-1/2√2 and so Z=1/2√2 as in Z x/lxl = 1

sry in Y .. it shud have been x--> -∞ and i have written ∞ .. sry

Oh okay..... tgnx asis