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NDA Math Limit, Continuity and Differentiability

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For the next two (2) items .that follow :
Consider the function
f(x)=

a[x]+x−1

[x]+x

where [·] denotes the greatest integer function.

[NDA I 2016]

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Question : 66

Total: 105

‌ What is ‌

f(x)‌ equal to? ‌

1
ln α
1−α−1
limit does not exist

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