Continuity lecture#1

The equation of continuity leads to

Continuity of germplasm' theory was given by

Discuss the continuity of the function f(x) = |x -1| at x=1

Discuss the continuity of the f(x) at the indicated point: f(x)=|x-1|+|x+1| at x=-1,\ 1.

Discuss the continuity of the function f, where f is defined by f(x)={{:(-2, ifxlt=-1),( 2x , if-1 1):}

Discuss the continuity of the function f defined by f(x) = 1/(x-1) , x ne 1

If f(x) = (x^(2)-1)/(x-1) Discuss the continuity at x rarr 1

For what value of lambda is the function f(x)={lambda(x^2-2x)\ \ \ \ ,\ \ \ \ if\ xlt=0 4x+1\ \ \ \ ,\ \ \ \ if\ x >0 continuous at x=0 ? What about the continuity at x=+-1 ?

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

Examine continuity of the function f(x) = x^(3) + 2x^(2)- 1 at x = 1 .