I'm hopelessly confused on these two questions, any help is appreciated!
1) 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
f(x) = 10x + e−x; g(x) =1/(5x)
f(x) = x2; g(x) = e−4x
f(x) =(Lnx)3; g(x) =1 divided by x
f(x) =square root of x; g(x) = e−x
2)If f(x) is differentiable for the closed interval [−1, 4] such that f(−1) = −3 and f(4) = 12, then there exists a value c, −1< c < 4 such that
f '(c) = 3
f '(c) = 0
f(c) = −15
f (c) = 3

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