Question

CALC!! Please help me. For which pair of functions f(x) and g(x) below will the limit as x goes to infinity of the product of f of x and g of x does not equal 0? (I have attached a photo of the multiple choice answers and the question itself)

Answer 1

First limit:

`\lim_(x\to\infty)(10x+e^(-x))*(1)/(5x)`

`=\lim_(x\to\infty)(2+(1)/(5xe^(x)))`

`=2+0`

`=2`

Since we know that the first pair of functions does not approach 0, we do not have to check the others.