If `f(x)={sin((a-x)/2)t h a n[(pix)/(2a)]forx > a([cos((pix)/2)])/(a-x)forx0,` then `f(a^-)<0` b. `f` has a removable discontinuity at `x=a` c. `f` has an irremovable discontinuity at `x=a` d. `f(a^+)<0`

Options

A. `f(a^(-))lt0`
B. f has a removable discontinuity at x = a
C. f has an irremovable discontinuity at x = a
D. `f(a^(+))lt0`

Answer

B

Explanation

`f(a^(-))=underset(hrarr0)(lim)([cos((pi)/(2a)(a-h))])/(h)=underset(hrarr0)(lim)([sin(pih)/(2a)])/(h)=0.`
`f(a^(+))=underset(hrarr0)(lim)(-(sin h)/(2))tan[(pi)/(2)+(pih)/(2)]=0,`
Hence `f(a^(+))=f(a^(-))`.
Thus, f(x) has removable discontinuity at x = a.