Subject: Two limits
How do I find
lim (1-cosx)/(x^2) as x-> 0
lim (tan3x)/x as x->0
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.
I also know that
and hence I can proceed as follows.
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.