Show that `f(x)={{:(x^(2),if, 0 le x le 1),(x ,if, 1 le x le 2):}` is continuous on [0,2]

Show that g (x) = {{:( x^(2) " if " x le 1), ( x " if " x gt 1):} is continuous or R .

If the function 'f' defined by f(x)={{:(kx+1,if,-1lex le1),(x^(2)-1,if, 1le x le2):} is continuous functo on [-1,2] then the find th value of K.

Find real contans, a b so that the function 'f' given by f(x)={{:(sinx , if, x le0),(x^(2)+a, if, 0 lt x lt 1),(bx+3,if, 1 le x le 3),(-3,if,x gt 3):} is continuous on R.

If f(x)={{:(x^(2) " for " 0 le x le 1),(sqrt(x) " for "1 le x le 2):} then int_(0)^(2) f(x)dx=

f(x) = {{:(4-3x " if " x le 0),(2a + x " if " x ge 0):} is continuous at x = 0 then a =

f(x)={{:(x^(2),if x le 1),(x, if 1 lt x le 2),(x-3,if x gt 2):} then Lt_(x to 2+) f(x)=