I have 3 very tricky limits questions
1 lim (x sin(x^2 e^x))/(x^2 1) as x approaches infinity.
2 lim(1/(e^x sin(1/x^2)) as x approaches infinity
3 lim(x-x^1/2 lnx) as x approaches infinity
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I have 3 very tricky limits questions
1 lim (x sin(x^2 e^x))/(x^2 1) as x approaches infinity.
2 lim(1/(e^x sin(1/x^2)) as x approaches infinity
3 lim(x-x^1/2 lnx) as x approaches infinity
You can try use de l'Hopital rule when dealing with limits of form:
1.
Notice that, thus
thus
2.
This is more tricky, you have to see who wins between(who goes to infinity) and
(who goes to 0). Using
you can have
thus
3. lim(x-x^1/2 lnx) as x approaches infinity
It does not display correctly (maybe a plus sign is missing), but both
and
converge to infinity.
You can verify this by using
or similarly
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