213k views
2 votes
F(x)=2x*e^2x. find lim of f(x) as x--> - infinity and +infinity ...?

User Hrdwdmrbl
by
7.4k points

1 Answer

7 votes
I am assuming it is f(x)=2x e^2x
2x times e raised to the 2x power, and not 2 times e raised to the 2x**

as it approaches infinity, your f(x) --> infinity
we can see by inspection, as 2x will approach inf, and e^(2x) will approach infinity even faster.
inf x inf = inf

as it approaches neg infinity, your f(x) --> 0
we can see by inspection, as 2x will approach neg inf, and e^(2x) will approach zero.
- inf x 0 = - 0

The minimum(or maximum) is given when the derivative = 0
Using the product rule,
f ' (x) = 2e^(2x) + 4x e(2x)
f ' (x) = 2e^(2x) ( 1 + 2x )
We find the roots
2e^(2x) will never equal 0
1 + 2x = 0, x = -1/2

The minimum value will be when x = -0.5
User Pauminku
by
8.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories