Question

Determine lim t->10 (((t^2)-100)/(t+1))(cos)(1/(10-t))+100

Answer 1

To confirm, is this the expression you wish to evaluate?\[\huge \lim_{t\rightarrow 10}\left[\frac{t^2-100}{t+1}\cos\left(\frac{1}{10-t}\right)+100\right]\]

Answer 2

yupp

Answer 3

Can you double-check that it isn't this?\[\huge \lim_{t\rightarrow 10}\left[\frac{t^2-100}{t+10}\cos\left(\frac{1}{10-t}\right)+100\right]\]

Answer 4

Whoops...sorry about that. It works just the same either way.\[\Large \lim_{t\rightarrow 10}\left[\frac{t^2-10}{t+1}\right]\lim_{t\rightarrow 10}\left[\cos\left(\frac{1}{10-t}\right)\right]+\lim_{t\rightarrow 10}\left[100\right]\]Two of these limits are evaluated easily by plugging in \(t=0\).\[\Large 0\cdot \lim_{t\rightarrow 10}\left[\cos\left(\frac{1}{10-t}\right)\right]+100\]Since the cosine function is bounded within the interval [-1,1], we can comfortably say \(0\cdot \lim_{t\rightarrow 10}\left[\cos\left(\frac{1}{10-t}\right)\right]=0\). This is not always the case so don't think you can do this every time! You can only do this when we have a bounded function we have still not evaluated the limit of.

Answer 5

Thanks alot! =)