Infinite Sequence and Series

[xstetsonx]

Got a couple questions please help!!

1. lim n>inf (x^4)/(e^(-2x))

How do you do this one??? i know you use L hospital rule but you can never get rid of the denominator. or is there a trick i am missing???

2. Determine whether the sequences are increasing, decreasing, or not monotonic.
1.(cos(x))/(3^x)
2.(x-3)/(x+3)
3.1/(3x+6)

can you explain what to do with this one???

[LCKurtz]

Got a couple questions please help!!

1. lim n>inf (x^4)/(e^(-2x))

How do you do this one??? i know you use L hospital rule but you can never get rid of the denominator. or is there a trick i am missing???


You mean x --> infinity? Why would you use L'Hospital's rule? You have an infinity / 0 form.

2. Determine whether the sequences are increasing, decreasing, or not monotonic.
1.(cos(x))/(3^x)
2.(x-3)/(x+3)
3.1/(3x+6)

can you explain what to do with this one???

You could look at their derivatives.