Which quadrants and axes does #f(x)=cos(sqrtx)# pass through?

1 Answer
Tamir E.
Nov 26, 2017

quadrants #I# and #IV# and both axes

(for #x in RR#)

Explanation:

If you work in #RR#:

#sqrtx in RR iff x>=0#
#=># quadrants #II# and #III# are not relevant...

#f_((0))=cos(sqrt0)=cos0=1#
#(0,1)#
#f_((x))=0 => cos(sqrtx)=0 => sqrtx=pi/2 =>x=pi^2/4>0#
#(pi^2/4,0)#
#=># both axes

#f_((pi/2))=cos(sqrt(pi/2))=+0.312175571143>0#
#f_(((5pi)/2))=cos(sqrt((5pi)/2))=-0.943055404868<0#
#=># quadrants #I# and #IV#

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