ratio limit theorem

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..

Limits of Trigonometric Functions and Sandwich Theorem: for all x in some open interval containing c and suppose Since f is sandwiched between two functions g and h, the above theorem is known as sandwich theorem..

The medians of a triangle pass through the same point which divides each of the medians in the ratio 2:..

Statement - The medians of a triangle pass through the same point which divides each of the medians in the ratio 2:..

A line parallel to one side of a triangle divides the other two sides into parts of equal proportion. In triangle ABC, a line drawn parallel to BC cuts AB and AC at P and Q respectively. Let the point P divide AB in the ratio of l: m where l and m are natural numbers. Divide AP into 'l' a..

Evaluation of definite integral by changing limits after suitable substitution. Step I : Let z = g(x) be the desired substitution, dz = g ' (x) dx Step II : when x = a, z = g(a) x = b, z = g(..

. Thus stable nuclei (non-radioactive) have n/p ratio between 1 - 1.6. These lie in the shaded region of the plot which is also called stability belt or stability zone. The elements whose nuclei do not fall within the stability zone are said to be unstable. The unstable nuclei, whose n/p ..

Let and In 30 o - 60 o - 90 o triangle, it can be proved that the hypotenuse is double the side opposite to 30 o (see proof in Geometry Section), AC = 2AB Let AB = a AC = 2a Using Pythagoras Theorem BC 2 = (2a) 2 - a 2 = 4a 2 - a 2 = 3a 2 ..

Before describing the limits of trigonometric functions, we state few theorems along with Sandwich theorem, which helps in calculating a variety of limits in subsequent chapter..

Limits- operations on functions Continuity of a function Intermediate value, extreme value theorem Derivatives, differentiability Derivatives of functions Chain rule Rolle's theorem, mean value theorem, and L'Hopital's rule Maxima, minima, inflection poin..