Let `f(x) = {:{(x+a,xle1),(ax^2+1,x>1):}`.
Find `a` so that f may be derivable at `x = 1`.

Let f(x) = {:{(x+a, x le1),(ax^2 + 1, x > 1):} . Show that f is continuous at 1. Find 'a' so that it is derivable at 1.

True or False : The function f(x) = {:{(x+a, xge1),(ax^2 +1, x <1):} is continuous at x = 1, whatever 'a' may be.

Let f(X) = {:{((x-1) tan (pi/2x), x ne 1),(k, x =1):} . Find k if f is continuous at x = 1.

if f(x) = {{:(x^2, x le 1),(ax + b ,x gt 1):} is differentiable at x = 1 . Find the values of a and b.

Let f(x) = {:{(ax+3,xle2),(a^2x-1,x>2):} . Then the value of 'a' for which 'f' is continuous for all x are

Find a,b so that the function f(x) = {:{(1,xle3),(ax +b, 3 < x < 5),(7,xge5):} may be continuous at x = 3 and x = 5

If f(x) = {{:(A+Bx^(2)",",x lt 1),(3Ax - B+2",",x ge 1):} , then A and B, so that f(x) is differentiabl at x = 1, are

Let f(x)={:{(6","xle1),(7-x","xgt1):} 'then for f(x) at x=1 discuss maxima and minima.

Let f (x) = x tan ^(-1) (x^(2)) then find the f'(x)

Find the values of a so that the function f defined by f(X) = {:{((sin^2ax)/x^2, x ne 0),(1, x = 0):} may be continuous at x = 0.