Limit questions

Question

Evaluate the limit..

Lim _x-->∞  2^x - 1 / x

 

Answer 1

If you mean exactly what it says then your answer is ∞, because 2^x is a very rapidly growng function and 1/x approaches zero. I think your expression is  (2^x - 1)/x and the limes of it is still ∞ for the same reason (1 can be ignored compared with 2 ^x ).Thus, we are dealing wih diverging functions when x → ∞.