Question #3ded9 Calculus Limits Intemediate Value Theorem 1 Answer Wataru Apr 1, 2017 Let #f(x)=x-cos x#. We know that #f# is continuous on #[0,pi/2]# since it is the difference of two continuous functions #x# and #cos x#, and #f(0)=-1<0< pi/2=f(pi/2)#. By Intermediate Value Theorem, there exists #c in (0,pi/2)# s.t. #f(c)=c-cos(c)=0#, which means that #c=cos(c)#. Hence, #x=cos x# has a solution #c in (0,pi/2)#. Answer link Related questions How do you verify the intermediate value theorem over the interval [0,5], and find the c that is... How do you verify the intermediate value theorem over the interval [0,3], and find the c that is... How do you verify the intermediate value theorem over the interval [0,3], and find the c that is... How do you verify the intermediate value theorem over the interval [5/2,4], and find the c that... See all questions in Intemediate Value Theorem Impact of this question 2774 views around the world You can reuse this answer Creative Commons License