Subject: Two limits
How do I find
lim (1-cosx)/(x^2) as x-> 0 and lim (tan3x)/x as x->0 Hi, Many of the limits in first semester calculus that involve trig functions revolve around one fundamental fact. That fact is
The problem then usually involves some algebraic and/or trigonometric manipulation to use this fact. As is often the case in algebra and trigonometry you need to see a pattern somewhere.
^{2} x = sin^{2} x.
I also know that
^{2} x = (1 - cos x)(1 + cos x)
and hence I can proceed as follows.
Thus
In your second problem tan3x = sin3x/cos3x and thus
For the first factor to be of the form sint/t so that you can apply the fact mentioned above you need t = 3x so multiply the numerator and denominator by 3 to get
Now take the limit as x->0.
Cheers, |