Discuss the continuity of the function:
f(x)={xtan-1(1/x), x≠0
{0, x=0 at x=0.

Dear Student,
Please find below the solution to the asked query:

fx=x.tan-11xx00x=0fx will be continuous at x=0, iflimx0 fx=f0Nowlimx0 fx=limx0x.tan-11xNow range of tan-1α is -π2 to π2, hence whatever be the value of α,  tan-1αwill always between -π2and π2, hence applying limit, we get,limx0 fx=0×Finite number between -π2and π2limx0 fx=0f0=0Aslimx0 fx=f0=0, hence fx is continuous at x=0.

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