Evalute the following limit if they exist 1 lim x5 x35x 2 li

Evalute the following limit if they exist

1. lim x5 x+3/5-x

2. lim x3 9-2x^2/x-3

3. limx9 x-3/x-9

Solution

1. lim _x5 x+3/5-x

lim _x5^- x+3/5-x =

lim _x5⁺ x+3/5-x =-

lim _x5^- x+3/5-x lim _x5⁺ x+3/5-x

so  lim _x5   x+3/5-x does not exist

2)lim _x3 9-2x^2/x-3

lim _x3^-   9-2x^2/x-3 =

lim _x3⁺     9-2x^2/x-3 =-

lim _x3^-     9-2x^2/x-3 lim _x3^-     9-2x^2/x-3

so lim _x3    9-2x^2/x-3 doesnot exist

3)lim_x9 ^(x-3)/_(x-9)

lim_x9   ^(x-3)/_(x²-3²)

lim_x9   ^(x-3)/_(x-3)(x+3)

lim_x9   ¹/_(x+3)

= ¹/_{(9 +3)}

=¹/₍₃₊₃₎

=¹/₆

lim_x9   ^(x-3)/_(x-9) =¹/₆