is the function f(x) = (3x+4tanx)/x continuous at x = 0? if not how may the function be defined to make it continuous at this point?

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

fx=3x+4tanxxAs denominator becomes 0 at x=0, hence function is not continuous at x=0.Hence make function continuous at x=0, we should define f0 such that:limx0 fx=f0Nowlimx0 fx=limx03x+4tanxx=limx03xx+4tanxx=limx03+4tanxx=3+4limx0tanxx=3+4       As limx0tanxx=1limx0 fx=7f0=7Hencefx=3x+4tanxxx07x=0

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