The function is feet/sec.
(a)
Find rate when is .
ft/sec.
(b)
(c)
Find limit as .
As tends to from the left hand side, the limit approaches to .
.
(a) ft/sec.
(b) ft/sec.
(c).
![\"\"](\"http://www.mathskey.com/userfiles/image/steps_images/step1.JPG\")
![\"r=50\\pi\\sec^2\\theta\"](\"http://latex.codecogs.com/gif.latex?r%3D50%5Cpi%5Csec%5E2%5Ctheta\")
feet/sec.![\"r\"](\"http://latex.codecogs.com/gif.latex?r\")
when ![\"\\theta\"](\"http://latex.codecogs.com/gif.latex?%5Ctheta\")
is ![\"\\frac{\\pi}{6}\"](\"http://latex.codecogs.com/gif.latex?%5Cfrac%7B%5Cpi%7D%7B6%7D\")
.![\"\\\\\\lim_{\\theta](\"http://latex.codecogs.com/gif.latex?%5C%5C%5Clim_%7B%5Ctheta%20%5Crightarrow%20%5Cfrac%7B%5Cpi%20%7D%7B6%7D%7Dr%3D%5Clim_%7B%5Ctheta%20%5Crightarrow%20%5Cfrac%7B%5Cpi%20%7D%7B6%7D%7D50%5Cpi%5Csec%5E2%5Ctheta%20%5C%5C%5C%5C%3D50%5Cpi%5Csec%5E2%5Cfrac%7B%5Cpi%20%7D%7B6%7D%20%5C%5C%5C%5C%3D50%5Cpi%5Cleft%20%28%20%5Cfrac%7B2%7D%7B%5Csqrt%7B3%7D%7D%20%5Cright%20%29%5E2%20%5C%5C%5C%5C%3D50%5Cpi%5Cleft%20%28%20%5Cfrac%7B4%7D%7B3%7D%20%5Cright%20%29%20%5C%5C%5C%5C%3D%5Cfrac%7B200%5Cpi%7D%7B3%7D\")
![\"\\\\\\lim_{\\theta](\"http://latex.codecogs.com/gif.latex?%5C%5C%5Clim_%7B%5Ctheta%20%5Crightarrow%20%5Cfrac%7B%5Cpi%20%7D%7B6%7D%7Dr%3D%5Cfrac%7B200%5Cpi%7D%7B3%7D\")
ft/sec.![\"\"](\"http://www.mathskey.com/userfiles/image/steps_images/step2.JPG\")
when is ![\"\\frac{\\pi}{3}\"](\"http://latex.codecogs.com/gif.latex?%5Cfrac%7B%5Cpi%7D%7B3%7D\")
.![\"\\\\\\lim_{\\theta](\"http://latex.codecogs.com/gif.latex?%5C%5C%5Clim_%7B%5Ctheta%20%5Crightarrow%20%5Cfrac%7B%5Cpi%20%7D%7B3%7D%7Dr%3D%5Clim_%7B%5Ctheta%20%5Crightarrow%20%5Cfrac%7B%5Cpi%20%7D%7B3%7D%7D50%5Cpi%5Csec%5E2%5Ctheta%20%5C%5C%5C%5C%3D50%5Cpi%5Csec%5E2%5Cfrac%7B%5Cpi%20%7D%7B3%7D%20%5C%5C%5C%5C%3D50%5Cpi%5Cleft%20%282%20%5Cright%20%29%5E2%20%5C%5C%5C%5C%3D50%5Cpi%5Cleft%20%5Cleft%20%28%204%20%5Cright%20%29\")
![\"=200\\pi\"](\"http://latex.codecogs.com/gif.latex?%3D200%5Cpi\")
![\"\\\\\\lim_{\\theta](\"http://latex.codecogs.com/gif.latex?%5C%5C%5Clim_%7B%5Ctheta%20%5Crightarrow%20%5Cfrac%7B%5Cpi%20%7D%7B3%7D%7Dr%3D200%5Cpi\")
ft/sec.![\"\"](\"http://www.mathskey.com/userfiles/image/steps_images/step3.JPG\")
![\"\\theta\\rightarrow](\"http://latex.codecogs.com/gif.latex?%5Ctheta%5Crightarrow%20%5Cfrac%7B%5Cpi%7D%7B2%7D%5E-\")
.![\"\\\\\\lim_{\\theta](\"http://latex.codecogs.com/gif.latex?%5C%5C%5Clim_%7B%5Ctheta%20%5Crightarrow%20%5Cfrac%7B%5Cpi%20%7D%7B2%7D%5E-%7D50%5Cpi%5Csec%5E2%5Ctheta\")
tends to ![\"\\frac{\\pi](\"http://latex.codecogs.com/gif.latex?%5Cfrac%7B%5Cpi%20%7D%7B2%7D%5E-\")
from the left hand side, the limit approaches to ![\"\\infty\"](\"http://latex.codecogs.com/gif.latex?%5Cinfty\")
.![\"\\\\\\lim_{\\theta](\"http://latex.codecogs.com/gif.latex?%5C%5C%5Clim_%7B%5Ctheta%20%5Crightarrow%20%5Cfrac%7B%5Cpi%20%7D%7B2%7D%5E-%7D50%5Cpi%5Csec%5E2%5Ctheta%3D%5Cinfty\")
.![\"\"](\"http://www.mathskey.com/userfiles/image/steps_images/solution.JPG\")
ft/sec. ft/sec..