Let : `f(x)={(sina x^2)/(x^2),x!=0 3/4+1/(4a),x=0` for what values of `a` is `f(x)` continuous at `x=0?`

Let f(x+(1)/(x) ) =x^2 +(1)/(x^2) , x ne 0, then f(x) =?

Let f(x)={(log(1+x)^(1+x)-x)/(x^2)}dot Then find the value of f(0) so that the function f is continuous at x=0.

If f(x)={(sin(2x^2)/a+cos((3x)/b))^a b//x^2,x!=0e^3, x=0 is continuous at x=0AAb in R then minimum value of a is -1//8 b. -1//4 c. -1//2 d. 0

Let f(x)=int x^2/((1+x^2)(1+sqrt(1+x^2)))dx and f(0)=0 then f(1) is

If f(x)={(1-cos(1-cos x/2))/(2^m x^n)1x=0,x!=0 and f(0)=1 is continuous at x=0 then the value of m+n is a. 2 b. 3 c. -3 d. 7

if f(x) = {(x^(3),x <0),(3a + x^(2), x ge 0):} is continuous at x = 0 , then a is

If f(x)=inte^(x)(tan^(-1)x+(2x)/((1+x^(2))^(2)))dx,f(0)=0 then the value of f(1) is

Let f(x) = xsqrt(4ax-x^(2)),(agt0) Then f(x) is

Let f(x)={x+1,x >0 2-x ,xlt=0 and g(x)={x+3,x 0)g(f(x)).

For what value of lambda is the function defined by f(x)={{:(lambda(x^(2)-2x)," if "x le 0),(4x+1," if "x gt 0):} continuous at x= 0? What about continuity at x =1?