If `g(x)=(1-a^x+x a^xloga)/(x^2*a^x), x<0` `((2a)^x-xlog(2a)-1)/(x^2), x >0` (where a > 0) then find a and `g(0)` so that `g(x)` is continuous at `x=0.`

If g(x)=(1-a^(x)+xa^(x)log a)/(x^(2)*a^(x)),x 0 (where a >0) then find a and g(0) so that g(x) is continuous at x=0.

Consider the function f(x)={(1-a^x+x a^x ln a)/(a^xx^2); x 0 where a > 0. If g(x) is continuous at x=0 then a=sqrt(2) (b) g(0)=1/8(ln2)^2 a=1/(sqrt(2)) (d) g(0)=1/2ln2

If f.g is continuous at x = 0 , then f and g are separately continuous at x = 0 .

Let g(x) be a polynomial of degree one and f(x) is defined by f(x)={g(x),x 0} Find g(x) such that f(x) is continuous and f'(1)=f(-1)

If f'(x)=g(x)(x-a)^(2), where g(a)!=0 and g is continuous at x=a, then :

Let f(x)=[x], where [.] is the greatest integer fraction and g(x)=sin x be two valued functions over R. Which of the following statements is correct? (a) Both f(x) and g(x) are continuous at x=0 (b) f(x) is continuous at x=0, but g(x) is not continuous at x=0. (c) g(x) is continuous at x=0, but f(x) is not continuous at x=0. (d) Both f(x) and g(x) are discontinuous at x=0

Let f(x) and g(x) be two equal real function such that f(x)=(x)/(|x|) g(x), x ne 0 If g(0)=g'(0)=0 and f(x) is continuous at x=0, then f'(0) is

Let f and g be real valued functions defined on interval (-1, 1) such that g'' (x) is continuous, g(0) ne 0, g'(0) = 0, g''(0) ne 0, and f(x) = g''(0) ne 0 , and f(x) g(x) sin x . Statement I lim_( x to 0) [g(x) cos x - g(0)] [cosec x] = f''(0) . and Statement II f'(0) = g(0).

If (x)={g^(x),x =0f(x)={g^(x),x =0 where [.1) denotes the greatest integer function. The f(x)

Let f and g be real valued functions defined on interval (-1,\ 1) such that g"(x) is continuous, g(0)!=0 , g'(0)=0, g"(0)!=0 , and f(x)=g(x)sinx . Statement-1 : ("Lim")_(x->0)[g(x)cotx-g(0)"c o s e c"x]=f"(0) and Statement-2 : f'(0)=g(0)