Which quadrants and axes does #f(x)=cos^2x# pass through?
↳Redirected from
"Find the limit as x approaches infinity of #xsin(1/x)#?"
#f(x)=cos^2x# is always #0# or positive and can take any value between #[0,1]# and it touches #x# at #x=(2k+1)pi/2# and passes only through #Q1# and #Q2#
#cosx# can take values only between #[-1,1]#, further when #x=2kpi# #cosx=1# and when #x=(2k+1)pi# #cosx=-1# and at #x=(2k+1)pi/2#, #cosx=0#
#f(x)=cos^2x# is always #0# or positive and can take any value between #[0,1]# and it touches #x#-axis at #x=(2k+1)pi/2#
Hence it passes only through #Q1# and #Q2#
and while it touches #x#-axis at #x=(2k+1)pi/2#, it crosses #y# axis at #x=0#
