continuous at a point in its domain if the limit of the function at that point equals the value of the function at that point. A function is continuous if it is continuous on the whole of its domain. ® Sum, difference, product and quotient of continuous functions are continuous. i.e., if f and g are continuous functions, then ( f ± g ) ( x ) = f ( x ) ± g ( x ) is continuous.
( f . g ) ( x ) = f ( x ) . g ( x ) is continuous. f g g x (wherever g ( x ) ≠ ) is continuous.
® Every differentiable function is continuous, but the converse is not true. ® Chain rule is rule to differentiate composites of functions. If f = v o u , t = u ( x ) and if both dt dx and dv dt exist then df dv dt dt dx