lim [x^2011 + 2010^x] / [-(x)^2010 + 2011^x]
x-->∞
just evaluate and show steps please L'hospitals rule is totally allowed. Just do something to get the answer.
The answer can be -1 , -∞ , ∞ , 0, or none of the above
Additional Details
PLEASE SHOW ANY STEPS, no calc allowed
x-->∞
just evaluate and show steps please L'hospitals rule is totally allowed. Just do something to get the answer.
The answer can be -1 , -∞ , ∞ , 0, or none of the above
Additional Details
PLEASE SHOW ANY STEPS, no calc allowed
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lim [x^2011 + 2010^x] / [-(x)^2010 + 2011^x] =
x-->∞
lim [2010^x] / [2011^x] =
x-->∞
lim (2010/2011)^x = 0, since 2010/2011 < 1
x-->∞
---------
Attn: x^2011 << 2011^x as x->∞. So, neglecting lower degree terms gives you the above answer. Try to learn some simple way to get it done.
x-->∞
lim [2010^x] / [2011^x] =
x-->∞
lim (2010/2011)^x = 0, since 2010/2011 < 1
x-->∞
---------
Attn: x^2011 << 2011^x as x->∞. So, neglecting lower degree terms gives you the above answer. Try to learn some simple way to get it done.
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The limit does not exist!
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I can't help, sorry.