Differential Calculus - Calculating Limits?

Question

Lim (3+5/x) = 3
x➝∞

because it is known that 5/x➝0 as x➝∞

Lim (6x+4/2x-9) =
x➝∞

collect x in the numerator and denominator

Lim x(6+4/x)/x(2-9/x) =
x➝∞

simplify x
Lim (6+4/x)/(2-9/x) = 6/2 = 3
x➝∞

Lim( x^2-4/x-2) = 0/0 is an indetermination form
x➝2

factor numerator

Lim (x+2)(x-2)/(x-2) =
x➝2

Lim (x+2) = 2 + 2 = 4
x➝2

similar to the previous one
Lim (x^2+x-12/x-3)
x➝3

Lim (x - 3) (x + 4)/(x - 3)
x➝3

Lim (x + 4) = 3 + 4 = 7
x➝3

Answer 1

(1). Lim (3+5/x) = 3
       x➝∞

because it is known that 5/x➝0 as x➝∞.

 

(2). Lim (6x+4/2x-9)
      x➝∞

collect x in the numerator and denominator

= Lim x(6+4/x)/x(2-9/x)
  x➝∞

Simplify x

= Lim (6+4/x)/(2-9/x) = 6/2 = 3
   x➝∞

 

(3).Lim( x^2-4/x-2) = 0/0 is an indetermination form
     x➝2

factor numerator

= Lim (x+2)(x-2)/(x-2)
   x➝2

= Lim (x+2) = 2 + 2 = 4
   x➝2

 

(4). similar to the previous one

Lim (x^2+x-12/x-3)
x➝3

Lim (x - 3) (x + 4)/(x - 3)
x➝3

Lim (x + 4) = 3 + 4 = 7
x➝3