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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 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 class=

Verified Answer :

bartdrinksmalk

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

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

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