How to solve limx→−∞ x⋅e^(−2x)=−∞ step by step?

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Answer 1 · 2018-05-03T05:29:10

See below.

We are given:

#lim_(x->-oo) x e^(-2x)#

There is property of limits where:

#=> lim_(x->a) {f(x) * g(x)} = lim_(x->a){f(x)} * lim_(x->a){g(x)}#

Hence,

#lim_(x->-oo){x} * lim_(x->-oo) {e^(-2x)}#

We can clearly see that the first term goes to negative infinity. How about the second limit?

#=> lim_(x->-oo) {e^(-2x)} -> oo #

This means we have:

#(-oo)(oo)#

which is just #-oo#.

This technically means the limit does not exist.