Function f(x) = (\frac{n^{2}}{m^{2}}) then – | MATH - LIMITS | SolveeIt

Function f(x) = $\frac{n^{2}}{m^{2}}$ then –

$\lim_{x \rightarrow 0}\frac{(\cos x - 1)(\cos x - e^{x})}{x^{n}}$ does not exist

$f:R \rightarrow R$ does not exist

Discontinuous at x = \frac{\pi}{2}

Both (1) & (3)

Answer

Both (1) & (3)

Explanation

$\underset { \mathrm { x } = \pi / 2 } { \mathrm { At } }$ LHL $\lim _ { h \rightarrow 0 }$ (π/2 – h) sin (π/2 – h) = π/2

RHL $\lim _ { h \rightarrow 0 }$ (π/2) sin (π + π/2 + h) = – π/2 so (1) & (3) are correct

Question: Function f(x) = \(\frac{n^{2}}{m^{2}}\) then –...