For the function `f(x)={((sin^(2)ax)/(x^(2))",","where " x ne 0),(1",", "when " x =0):}` which one is a true statement

Options

A. f(x) is continuous at x = 0
B. f(x) is discontinuous at x = 0, when `a ne pm 1`
C. f(x) is continuous x = a
D. `lim_(x to 0) f(x) =f(0)`

Answer

B

Explanation

Given, `f(x) ={((sin^(2)a x)/(x^(2))",",x ne 0),( 1",", x =0):}`
Now, ` lim_( x to 0) f(x) =(sin^(2) ax)/((ax)^(2))a^(2) =a^(2) and f(0) =1`
Hence, f(x) is discontinuous at x = 0, when ` ne pm 1`.