Question

Example 2: Show that the limit value of g(y) = [2y 5] does not exist when y tends to 2. Solution: The given function is g(y) = [2y 5]. Clearly, g(y) is a greatest integer function Hence, Where, a is an integer The limit of g(y) when y tends to 2 is calculated as follows: y 1.9 1.95 1.99 1.999 2.001 2.01 2.05 2.1 g(y) 2 2 2 2 1 1 1 1 We may observe that Left hand limit of the function = whereas the right hand limit =. Since the left hand and the right hand limits of the function are not equal, the given function does not have a limiting value. I m totally not understanding this

Answer 1

as we know that if the function does not exist then right hand limit will not be equal to left hand limit
lim y tends to 2 (2y5)
"2*2*5