Evaluate the limit function and find its limit

Question

lim              √(1+t)-√(1-t)

t→0                     t

 

subsitution brought me to  √(1+0)-√(1-0)=            √(1)-√(1)=                   1-1=             0
                                              0                                 0                            0                 0

I think that im supposed to multiply the top and bottom by the squares but not sure.PLEASE ADD STEPS ON HOW TO GET TO THE ANSWER. 

Answer 1

There are a number of approaches to this problem.   The approach using the least sophisticated methods is to

multiply both top and bottom by √(1+t) + √(1-t).

 

  The numerator becomes  (1+t) - (1-t)     =  2 t

         while the denominator becomes   t (√(1+t) + √(1-t) )

 

    The factors of t upstairs and downstairs cancel leaving      2/ (√(1+t) + √(1-t) )

 

   The limit of this as t approaches zero is not an indeterminate form, so the limit is evaluated simply by replacing

t  by the point of interest (namely t =0)   to yield  2/2 = 1