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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)

CALC Please help me For which pair of functions fx and gx 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 class=
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Respuesta :

bartdrinksmalk
First limit:
[tex]\lim_{x\to\infty}(10x+e^{-x})*\frac{1}{5x}[/tex]
[tex]=\lim_{x\to\infty}(2+\frac{1}{5xe^{x}})[/tex]
[tex]=2+0[/tex]
[tex]=2[/tex]

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

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