00:01
In this problem, the first question is to evaluate limit extends to infinity x times 2 tan inverse x minus pi using l hospital's rule.
00:13
Now here this limit is of the form infinity times 0 to apply l hospital's rule.
00:22
We need to change it to either infinity by infinity form or 0 by 0 form.
00:27
So here we can rewrite limit x tends to infinity x times 2 tan inverse x minus pi as limit x tends to infinity 2 tan inverse x divided by 1 by x now it is converted to the 0 by 0 form and this can be evaluated using l hospital's rule.
00:55
Now using l hospital's rule, take the derivative of the numerator and denominator separately to get 2 times 1 by 1 plus x squared divided by negative 1 by x square.
01:11
Now this is limit x tends to infinity.
01:17
2 negative to x squared divided by 1 plus x square.
01:22
Now this is limit extends to infinity.
01:26
Negative 2 x squared divided by take x square common factor from the denominator to get 1 by x square plus 1.
01:35
So this x square in the numerator and denominator get cancelled and this becomes limit extends to infinity.
01:42
Negative 2 by 1 by x square plus 1.
01:46
Now applying the limit we have this term tends to 0...