mean value theorem sin

Rolle's Theorem - Let f be a real valued function in [a,b] such that f is continuous in [a,b]. f is differentiable in (a,b..

Theorem 7: - Let f be real valued function in [a,b] such that, f is continuous in [a,b]. f is differentiable in (a,b..

Let f be continuous on [a, b] and differentiable on the open interval (a, b). Then (a) f is increasing on [a, b] if f '(x) > 0 for each x (a, b) (b) f is decreasing on [a, b] if f '(x) < 0 for each x (a, b) This theorem can be proved by using Mean Value ..

AC can be defined in terms of the heat produced in a resistor due to motion of charges. The effective value (I r m s or I e f f ) of the AC is defined as the value of that direct current which produces the heat at the same rate as the alternating current in a given resistor. The..

Let f be a continuous function on an interval I = [a, b]. Then, f has the absolute maximum value and f attains it at least once in I. Also, f has the absolute minimum value and attains it at least once in ..

Since a velocity gradient exists across the tube, the mean velocity of the liquid is to be considered. The viscous drag which comes into play when the liquid is in motion, is not taken into account. In above conservation principle, part of K.E. is converted into heat..

If f(x) is a polynomial in x and is divided by x-a; then the remainder is is the value of f(x) at x = a i.e., remainder = f(..

If f(x) is a polynomial in x and is divided by x-a; the remainder is the value of f(x) at x = a i.e., Remainder = f(a..