1.lim(3x²-x+5)=3·2²-2+5=12-2+5=15
x->2
2.lim(x²-5x+6)/(3x²-9x)=lim(x-2)(x-3)/3x(x-3)=lim(x-2)/3x=(3-2)/9=1/9
x->3 x->3 x->3
3.lim(√2-x-√2+x)/x =lim(
√2-x-√2+x)(√2-x+√2+x) x=lim(2-x-x-2)/x=
x->0 x->0
=lim(-2x)x=-2
x->0
4.lim(5x³+x-1)(2x³-5x²)=lim(
(5x³+x-1)x³/(2x³-5x²)/x³=lim(5+1/x²-1/x³)/
x->∞ x->∞ x->∞
=
lim(5+1/x²-1/x³)/(2-5/x)=5/2=2.5
x->∞
5.lim√(x²+4)/3x=lim(x√1+4/x²)/3x=1/3
x->∞ x->∞