Limits and Continuity | Finding the value of a constant using limits

What is the limit with regards to continuity? Answer: A limit refers to a number that a function approaches as the approaching of an independent variable of the function takes place to a given value. For example, given the function f (x) = 3x, the limit of f (x) as the approaching of x takes place to 2 is 6.

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[MathsByPushkarSir]

I don't understand what's the point in changing the limits . In place of tan(x-2) write x-2 only as argument approaching zero as x tends to 2 . Further by observation denominator is (x-2)^2 . Eventually expression reduced to x^2+(k-2)x -2k divided by x-2 use l hospital rule and we are done