prove 1/infiity = 0

Question

prove that 1/infinity is equal to zero using definition of a derivative 

Answer 1

Let    f(x) = 1/∞

 

where x=∞

 

Definition of derivative:

 

lim         f(x + h) - f(x)      

h-->0   ______________      

                   h

 

 

lim        [1 / (∞ + h)] - (1 / ∞)

h-->0    __________________

                            h

 

 

              ∞ - (∞ + h)

lim       ______________ *        1

h-->0       ∞(∞ + h)             _______

                                                h

 

 

lim                 h

h-->0      ___________

                ∞(∞ + h)h

 

 

lim              1

h-->0      _______

               ∞² + ∞h

 

 

lim               1

h-->0     _________

               ∞(∞ + h)

 

 

 

Plug in h=0.

 

lim           1

h-->0    _____

                ∞²

 

 

lim       = 0

h-->0