If `R to R` is defined by
`f(x)={((2 sinx-sin2x)/(2x cos x)",","if "x ne 0),(a",","if " x =0):}`
then the value of a so that f is continuous at x = 0 is

Let f(x)={((cos^(2)x-sin^(2)x-1)/(sqrt(x^(2)+4)-2)"," , x ne 0),(a",", x =0):} , then the value of a in order that f(x) may be continuous at x = 0 is

If f(x) = ((a+x)^(2)sin(a+x)-a^(2)sin a)/(x) , x !=0 , then the value of f(0) so that f is continuous at x = 0 is

Consider the function f:R to R defined by f(x)={((2-sin((1)/(x)))|x|,",",x ne 0),(0,",",x=0):} .Then f is :

If f (x) = x sin (1)/(2), x ne 0 then the value of the ltbRgt function at x = 0 so that the function is continuous at x= -0 , is :

Let f(x)=(log (1+x+x^2)+log(1-x+x^2))/(sec x-cosx) , x ne 0 .Then the value of f(0) so that f is continuous at x=0 is

For what value of k, the function defined by f(x)={((log(1+2x)sin x^(@))/(x^(2))",", "for "x ne 0),(k",","for "x =0):} is continuous at x = 0 ?

If f(x)=x sin ((1)/(x)),x ne 0 then the value of the function at x=0, so that the function is continuous at x=0 is

Show that the function defined by f(x) = {{:(x^(2) sin 1//x",",x ne 0),(0",",x = 0):} is differentiable for every value of x, but the derivative is not continuous for x =