Examine the continuity of the following functions at indicated points.
`f(x)=sinfrac{pi[x]}{2}atx=0`

Examine the continuity of the following functions at indicated points. f(x)={(xsinfrac{1}{x}if xne0 atx=0),(0 if x=0):}

Examine the continuity of the following functions at indicated points. f(x)={(frac{[x]}{x}ifxne0 at x=0),(0 if x=0):}

Examine the continuity of the following functions at indicated points. f(x)={(sinfrac{1}{x}if xnea),(0 if x=0 atx=0):}

Examine the continuity of the following functions at indicated points. f(x)=[3x+11]atx=-11/3

Examine the continuity of the following functions at indicated points. f(x)={((sin2x)/x if xne0 at x=0),(2 if x=0):}

Examine the continuity of the following functions at indicated points. f(x)={(1/(x+[x])ifxlt0),(-1 if xge0):}

Examine the continuity of the following functions at indicated points. f(x)={((x^2-a^2)/(x-a),if xnea atx=a),(a, ifx=a):}

Examine the continuity of the following functions at indicated points. f(x)=(g(x)-g(1))/(x-1)atx=1 where g(x)=|x-1|

Examine the continuity of the following functions at indicated points. f(x)={(1/(e^(1/2)-1)ifxgt0 at x=0),(0 if xle0):}

Examine the continuity of the following functions at indicated points. f(x)={((1+2x)^(1/2)if xne0),(e^2 if x=0 at x=0):}