Lim/x--->3 x-3/x2-8x+15

Question

Lim/x--->3 x-3/x2-8x+15

Answer 1

Разложим знаменатель на множители: x^2-8x+15=x^2-8x+15+1-1=(x^2-8x+16)-1=(x-4)^2-1=(x-4-1)(x-4+1)=(x-5)(x-3).
lim/x-->3 (x-3)/(x-5)(x-3)=lim/x-->3/ 1/(x-5)=-1/2.

Answer 2

X^2-8x+15=x^2-8x+15+1-1=(x^2-8x+16)-1=(x-4)^2-1=(x-4-1)(x-4+1)=(x-5)(x-3).
lim/x-->3 (x-3)/(x-5)(x-3)=lim/x-->3/ 1/(x-5)=-1/2. фух