The value of $$L=\lim _{x \rightarrow[a]^{+}} \frac{\mathrm{e}^{\{x\}}-\{\mathrm{x}\}-1}{\{\mathrm{x}\}^{2}}$$ can be:
(A) $[a]$
(B) $2$
(C) $\{a\}$
(D)$\frac12$
where where [.] and {⋅} denotes greatest integer and fractional part function respectively
The given answer is (C) and (D).
For $h\to0^+, \{[a]+h\}=h$ :
So limit can be written as $$\lim _{h\to0^+} \frac{\mathrm{e}^h-h-1}{h^2}$$ which gives $L=\dfrac12$
But I have been unable to figure out how to get (C).