Question

# Find the value oflimx→ 2[x], where [x] represents greatest integer less than or equal to x. 2 3 None of these 1

Solution

## The correct option is C None of these lets look at the greatest integer before we solve this. The graph of [x] looks like. We can see that  the garph breaks at every integer points. We want to find limx→ 2[x] We will find left hand limit (limx→ 2−f(x)) and Right hand limit (limx→ 2+f(x)) separately, because the garph breaks at the point where we want to find the limit. (limx→ 2−f(x))=limh→ 0f(2−h)=1  & (limx→ 2+f(x))=limh→ 0f(2+h)=2 Since, Both limits are not equal the limit doesn't exist. Note - In greatest integer function limit doesn't exist at any integer point.

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