Question

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

Answer 1

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

You may have to find the product of f(x) and g(x) in each case and then determine whether or not this product approaches some limit other than 0 as x goes to infinity. I'd have to do that myself to determine which answer is correct.

Answer 2

I think you can find the limit of each function individually, and the pair where neither limit is 0 is right.

Answer 3

saves a little time on the algebra

Answer 4

Agreed. Suggest enclosing each function within parentheses if you do that.

Answer 5

Thank you to both of you!! @mathmale @peachpi

Answer 6

You're very welcome!!

What's the topic of the 2nd question? Can you recognize it?

Answer 7

I believe it is the Mean value theorem but the examples in my lesson only showed ones with function equations so im lost on how to do that one @mathmale