Does the following intergral converge or diverge? the integral from zero to infinity of ((x)^(1/2))*(e^(-x))

Question

Explain your reasoning, Please

 

Step by Step

Answer 1

a quick examination, x^(1/2) looks like it  will grow positive slower than e^(-x) grows smaller.  So e^(-x) will merge to 0.  Convergent.

 

Actually....Regardless of what is going on, on the left side, e^(-x) will approach 0 and anything multiplied by 0 is 0, right?