Number of points of $$non-differentiability$$ of the function $$gx=x2cos24x+x2cos24x+x2sin2$$⁡$$4x+x2cos2$$⁡$$4x+x2cos2$$⁡$$4x$$ in $$($$−$$50$$,$$50)$$ where [x] and $${x}$$ denotes the greatest integer function and fractional part function of x respectively, is equal to

Question

Number of points of $$non-differentiability$$ of the function $$gx=x2cos24x+x2cos24x+x2sin2$$⁡$$4x+x2cos2$$⁡$$4x+x2cos2$$⁡$$4x$$ in $$($$−$$50$$,$$50)$$ where [x] and $${x}$$ denotes the  greatest integer function and fractional part function of x respectively, is equal to

Infinity Learn · Accepted Answer

consider, $$g(x)=x2cos2$$⁡$$4x+x2cos2$$⁡$$4x+x2cos2$$⁡$$4x+x2cos2$$⁡$$4x+x2sin2$$⁡$$4x=x2+x2cos2$$⁡$$4x+cos2$$⁡$$4x+x2sin2$$⁡$$4x=x2cos2$$⁡$$4x+x2sin2$$⁡$$4x$$   (for$$ eg. $$2.25=2$$ and $$2.25=0.25$$ then $$2.25+$$ $$2.25$$ $$=2.25)=x2$$ Clearly $$g(x) is continuous and differentiable ∀x∈ℝNumber of points of $$non-differentiability$$ is ‘$$0$$’Therefore, the correct answer is $$0.00$$.

Differentiability

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Differentiability

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Number of points of non-differentiability of the function gx=x2cos24x+x2cos24x+x2sin2⁡4x+x2cos2⁡4x+x2cos2⁡4x in (−50,50) where [x] and {x} denotes the greatest integer function and fractional part function of x respectively, is equal to

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