यदि `2f(x)-3f((1)/(x))=x^(2)(xne0)`, तब `f(2)=`

If f(x) is an even function and satisfies the relation x^(2)f(x)-2f(1/x)=g(x),xne0 , where g(x) is an odd function, then find the value of f(2).

Let f(x)={{:((1)/(x^(2))sin(x^(2))," when "xne0),(0," when " x=0):} Discuss the continuity of f (x) at x = 0 .

If f(x) = x^2+1/x,xne0 then f(1/x) =

If : f((x^(2)+1)/(x))=(x^(4)+1)/(x^(2))," where "xne0," then: "f'(3)=

Let f(x)= {(((xsinx+2cos2x)/(2))^((1)/(x^(2))),,,,xne0),(e^(-K//2),,,,x=0):} if f(x) is continous at x=0 then the value of k is

Discuss the continuity of the function : f(x)={{:((1-cosx)/x^(2)", "xne0),(1", "x=0):} at x = 0.

Given , f(x)={{:((1-cos3x)/(x^(2)),"when " xne0),(1,"when "x=0):} Prove that f (x) is discontinuous at x = 0 .

If the following function f (x) is continuous at x = 0 , find k : f(x)={{:((1-cos2mx)/(2x^(2)),"when " xne0),(" " k,"when " x =0):}

If f(x)={{:(xsin((1)/(x))", if "xne0),(0" , if "x=0):} then at x=0 the function f is