The funtion f(x) is defined as follows:
`f(x) = {:{(x^2+ax+b,0lex<2),(3x+2,2lexle4),(2ax+5b,4 < xle8):}` If f(s) is continuous on [0,8], find the values of 'a' and 'b'.

The function f defined as f(x) = {{:((sin x^(2))/x ,x!=0 ),( 0 , 0):} is :

If a function f(x) is defined as f(x) = {{:(-x",",x lt 0),(x^(2)",",0 le x le 1),(x^(2)-x + 1",",x gt 1):} then a. f(x) is differentiable at x = 0 and x = 1 b. f(x) is differentiable at x = 0 but not at x = 1 c. f(x) is not differentiable at x = 1 but not at x = 0 d. f(x) is not differentiable at x = 0 and x = 1

For what value of 'a' and 'b', the function 'f' defined as: f(x) = {:{(3ax+b,ifx 1):} is continuous at x =1

The function f is defined by : f(x)= {(1-x,x 0):} . Draw the graph of f (x).

A function f(x) is defined by, f(x) = {{:(([x^(2)]-1)/(x^(2)-1)",","for",x^(2) ne 1),(0",","for",x^(2) = 1):} Discuss the continuity of f(x) at x = 1.

Examine the differentiability of the function 'f' defined by: f(x) = {:{(2x+3,if-3lex <-2),(x+1,if-2lex<0),(x+2,if0lexle1):}

Show that the function 'f' defined as follows, is continuous at x = 2, but not differentiable there at: f(x) = {:{(3x-2,0 2):}

Examine for continuity, the function 'f' defined by f(x) = {:{(e^(1//x), x ne 0),(0,x=0):} at x = 0

Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2 - ax + 1)/(x^2+ax+1) ;0 lt a lt 2 . Which of the following is true ?