Limit questions

Question

Evaluate the limit..

Lim _x-->0    (1+Δx)^1/2 - (1-x)^1/2 / x

 

 

Answer 1

For the expresssion shown the lim is infinity. Make sure the expression is correct.

I think it should be

           lim _x→ 0  [(1+x) ^1/2 -(1-x)^1/2]/x  

Multiply the numerator and denominator by [(1+x)^1/2 + (1-x)^1/2]. You will obtain in the numerator (after simplifying the expression)

                                         1+x -(1-x) = 2x

Then we can write

                                  lim x→0   2x/x[(1+x)^1/2 +(1-x)^1/2] = 2/2 = 1  (free x-s cancel each other)