Determine the values of a so that the funtion is continuous at x=1.
`f(x)=x^2+4` when `xle2`.
`=x^2+a^2`, when `xlt1`.

Determine the values of x for which the following functions fails to be continuous or differentiable f(x) = {((1-x), x lt 1), ((1-x)(2-x), 1lexle2 ), ((3-x), x gt 2):}

Find the cofficients a and b such that the following function f is continuous and differentiable at x=+-1: f(x)={{:((1)/(|x|)," when "|x|ge1),(ax^(2)+b," when " |x|lt1):}

A function f(x) is defined as follows : f(x)=-x," when "x lt0 =2," when "0 lex lt2 =4-x," when "x ge2 Draw the graph of the function and from the graph examine whether f(x) is continuous at x = 0 and x = 2 or not.

The value of f(0) so that the function f(x)=frac(2x-sin^-1x)(2x+tan^-1x is continuous at each point in its domain is equal to

Let f(x) ={{:((1-cos 4x)/(x^(2))",","when" x lt 0),(a",","when"x=0),((x)/(sqrt(16+sqrtx)-4)",","when" x gt0):} Determine the value of a, if possible, so that f(x) is continuous at x=0.

find the values of a and b , such that f(x) ={ax^2+1,xle1 and x^2+ax+b , x gt1 is differentiable at x=1

Show that Roll's theorem is not applicable to the following function in the interval 0 le x le 2 : f(x)={(" "2x" when " x le 1),(4-2x" when "x gt 1):}

A function f (x) is defined as follows : f(x)={{:(2-x",","when "xlt1),(x^(2)-3x",","when "xge1):} Examine the differentiability of the function f (x) at x= 1 , hence state whether f (x) is continuous at x = 1 or not .

The points of discontiuties of the funtion f(x)= (x+2)/(2x^2 - x - 1) are:

If the following function f (x) is continuous at x = 0 , find k : f(x)={{:((1-cos2mx)/(2x^(2)),"when " xne0),(" " k,"when " x =0):}