Show that f(x)=cos x is continuous for all values of x. – InterviewSolution

InterviewSolution

1.	Show that f(x)=cos x is continuous for all values of x.
Answer» Let x=a be any value . At x=a f(a)=cos a R.H.L `underset(xrarr0)limf(x)=underset(hrarr0)limf(a+h)` `=underset(hrarr0)lim cos (a+h)=cos a` `L.H.L=underset(xrarra^-)(lim)f(x)=underset(hrarr0)limf(0-h)` `=underset(hrarr0)limcos(a-h)=cosa` `therefore` R.H.L =f (a) =L.H.L and a is arbitrary value of x. `therefore` f(x) =cos x is continous for all values of x. Hence proved

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