Let f:R→R be a function given by f(x) = { 1-cos2x/x2, x≤0, a, x=0, β√1-cos2x/x, x ≥0, where α, β

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Show that the function: f(x)= x^2 *sin(1/x) at x!=0 f(x)= 0 at x=0 is continuous at x=0 ?#shorts Show that the function: f(x)= x^2 *sin(1/x) at x!=0 f(x)= 0 at x=0 is continuous at x=0 ?#shorts
Q) Let f:R→R be a function given by𝑓(𝑥)={((1−cos2𝑥)/𝑥^2 ,𝑥=0 𝛼 𝑥=0, (𝛽√(1−cos𝑥))/𝑥,&𝑥=0 Q) Let f:R→R be a function given by𝑓(𝑥)={((1−cos2𝑥)/𝑥^2 ,𝑥=0 𝛼 𝑥=0, (𝛽√(1−cos𝑥))/𝑥,&𝑥=0
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Let{.}denote fractional part of x and f(x)=cos^(-1) (1-{x}^2) sin^(-1) (1-{x}) /{x} -{x}^3 , x=0If L Let{.}denote fractional part of x and f(x)=cos^(-1) (1-{x}^2) sin^(-1) (1-{x}) /{x} -{x}^3 , x=0If L