lim(x->； ∞) ( 1+x+3x^2)/(x^2-2x-3)

The numerator and denominator are divided by x 2 at the same time

= lim(x->； ∞)( 1/x^2+ 1/x+ 3)/( 1-2/x-3/x^2)

= 3

(2)

lim(x->； ∞)( 1+x^2-x^3)/(6x^3-2x^2-3)

The numerator and denominator are divided by x 3 at the same time

= lim(x->； ∞)( 1/x^3+ 1/x- 1)/(6-2/x-3/x^3)

=- 1/6

(3)

let

3/x = 1/y

lim(x->； ∞) ( 1+3/x) ^(2x)

= lim(y->； ∞) ( 1+ 1/y) ^(6y)

=e^6

(4)

let

1/y = 1/(2x)

lim(x->； ∞) [ 1- 1/(2x) ] ^(3x)

= lim(y->； ∞) ( 1- 1/y) ^(3y/2)

=e^(-3/2)

(5)

lim(x->； 0) sin6x/x

= lim(x->； 0) 6x/x

=6

(7)

|sinx|≤ 1

lim(x->； ∞) ( 1+3x^2)/(x^3-2x+3) =0

= & gt

lim(x->； ∞) ( 1+3x^2).sinx/(x^3-2x+3) =0