JEE MainMathematicsModerateLimit

If $f(x) = \frac{x - e^{x} + cos2x}{x^{2}},x \neq$ is continuous
at x=0 (where denotes greatest integer function and denotes
fractional part function) then a

Show answer and solution

\lim_{x \rightarrow 0}\mspace{2mu}\frac{1 + x - e^{x} + (cos2x - 1)}{x^{2}} = \lim_{x \rightarrow 0}\mspace{2mu}\left( \frac{x - e^{x} + 1}{x^{2}} - \frac{(1 - cos2x)}{x^{2}} \right)

\Rightarrow + \ldots\cdots \rightarrow

\Rightarrow - 2 = - 5/2 = f(0)$$

Source: Grass-G / M-19 Mathematics Paper 28 Nov Fourth.docx

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