Solve the mathematical problem of finding the limit of function

( 1)

Upper and lower partition x 2

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

=( 1+0-0)/3( 1-0)^2

= 1/3

(2) up and down divided by X 3

=lim(2/x)/(3- 1/x^2+9/x^3)

=0/(3-0+0)

(3) divide x up and down.

=lim(x-4-7/x)/( 1-8/x)

= (infinity -4-0)/ 1

= infinity

④ Divided by (2x)^50 up and down

=lim( 1- 1/2x)^20( 1/(2x)^29+6/(2x)^30)/( 1-3/2x)^50

= 1*(0+0)/ 1

(5) Molecules are physical and chemical, and the denominator of molecules is multiplied by the radical sign (x 2-1)+x.

=lim [x (radical number (x 2-1)-x) (radical number (x 2-1)+x)]/(radical number (x 2-1)+x)

=lim x(- 1)/ (radical sign (x 2-1)+x)

Divide x up and down equally.

=lim (- 1)/[ radical sign (1-1/x 2)+1]

=- 1/( 1+ 1)

=- 1/2

(6) Molecules are physical and chemical

The numerator and denominator are multiplied by the root sign (x 4- 1)+x 2.

=lim (radical number (x 4- 1)-x 2) (radical number (x 4- 1)+x 2)/ (radical number (x 4- 1)+x 2)

=lim (- 1)/ (radical sign (x 4-1)+x 2)

=- 1/ (infinity+infinity)