For the function f(x)={((sin^(2)ax)/(x^(...

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

A

(a) f(x) is continuous at x = 0, when `a != +- 1`

B

(b) f(x) is discontinuous at x = 0, when `a != +- 1`

C

(c) `lim_(x to 0)f(x) = a`

D

(d) `lim_(x to 0)f(x) = a^(3)`

Verified by Experts

The correct Answer is:

B

Similar Questions

Explore conceptually related problems

If f(x)={((1)/(e^(1/x)+1),",","when" x != 0),(0,",","when"x = 0):} , then

If f(x)={(x^(2)(sin)1/x,",","when" x != 0),(0,",","when"x = 0):} , then

If f(x) ={((x-|x|)/x,",","when"x != 0),(2,",","when"x = 0):} , then

The function f(x)={{:(,(e^(1/x)-1)/(e^(1/x)+1),x ne 0),(,0,x=0):}

If the function f(x)={{:((x^(2)-1)/(x-1), "When ", x ne1),(k, "When" , x=1):} is given to be continuous at x=1 , then the value of k is ____.

If f(x) = {((sin 2x)/(5x), ",", "when" x != 0),(k, ",", "when" x = 0):} is continuous at x = 0, then the value of k will be

If the function f(x) defined by {:(f(x),=x sin(1/x),",","for"x != 0),(,=k, ",","for"x = 0):} is continuous at x = 0, then k =

If f(x)={(x,"when "0le x le 1),(2x-1,"when "x gt 1):} then -

Let f(x)={((sin pix)/(5x)",",x ne0),(k"," , x =0):} if f(x) is continuous at x = 0, then k is equal to

f(x) = {{:((|x|)/(x)",",x ne 0),(0",",x = 0):}