please solve this question and also show the steps of solution

1) Lim x->0 x^(2sinx)

ie lim x tends to 0, x to the power 2sinx

2) is L-hospitals rule valid for 0 to the power 0 condition

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- Jun 21st 2009, 10:14 AMayushhelp me in this kind of questions
please solve this question and also show the steps of solution

1) Lim x->0 x^(2sinx)

ie lim x tends to 0, x to the power 2sinx

2) is L-hospitals rule valid for 0 to the power 0 condition - Jun 21st 2009, 10:30 AMapcalculus
Set and take the log of both sides:

The limit of the right hand side as x goes to zero can be found using L'Hopital's Rule. (verify conditions)

So the limit as x tends to 0 of

Note that the limit of is 1, so you're left with

, whose limit is 0.

But remember that we just measured the limit of equal to 0, which means the limit of y, your original expression, is 1. Verify numerically and graphically.

Good luck!! - Jun 21st 2009, 10:59 AMayushplease help me in this question also
lim

x->infinity ((1+1/x^2)/x)

please tell the steps also - Jun 21st 2009, 11:16 AMapcalculus
- Jun 21st 2009, 11:18 AMHallsofIvy