[(ii)quad f(x)={[2x-1,," if ",x<=0],[2x+1,," if ",x>=0]],[" at "quad x=0]

Define f(x) as the product of two real functions f_(1)(x)=x, x epsilon R and f_(2)(x)={("sin"1/x, "if", x!=0),(0 , "if", x=0):} as follows f(x)={(f_(1)(x).f_(2)(x), "if", x!=0),(0, "if", x=0):} Statement 2: f_(1)(x) and f_(2)(x) are continuous on IR.

Determine if f defined by f(x)={x^2sin1/x , if""x!=0 0, if""""x=0

Discuss the continuity of f(x)={2x-1,quad x =0 at x=0

A function f(x) is defined as follows : f(x)={(x^(2)"sin"(1)/(x)", if "x!=0),(0", if "x=0):} show that f(x) is differentiable at x=0.

Examine the contiunity of the following functions at the indicated points . f(x) = {[2x+1 ,if xle0],[x, if 0 < x < 1],[2x-1,if xge1]:} at x=0,1.

Deine F(x) as the product of two real functions f_1(x) = x, x in R, and f_2(x) ={ sin (1/x), if x !=0, 0 if x=0 follows : F(x) = { f_1(x).f_2(x) if x !=0, 0, if x = 0. Statement-1 : F(x) is continuous on R. Statement-2 : f_1(x) and f_2(x) are continuous on R.

Discuss the continuity of f(x)={2x-1,\ \ \ x<0 ; {2x+1,\ \ \ xgeq0 at x=0

f(x)={(x^2 sin (1/x), xne0 ),(0, x=0):} at x=0

Test continuity for the folowing functions. f(x)={(2^(1/x), x ne0),(3,x=0):} at x=0