Question

求解这两题详细步骤！谢谢

Answer 1

lim_(x->0) ( (sin αx)^2 - (sinβx)^2 )/(x sinx)
=lim_(x->0) ( (αx)^2 - (βx)^2 )/x^2
=α^2 -β^2

let t=1-x
lim_(x->1) (1-x) tan(πx/2)
=lim_(t->0) t tan(π(1-t)/2)
=lim_(t->0) t sin(π(1-t)/2)/cos(π(1-t)/2)
=lim_(t->0) t /cos(π(1-t)/2)
=-lim_(t->0) 1 /( sin(π(1-t)/2) *(-π/2) )
=2/π