the central limit theorem implies

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..

Carnot engine is a reversible engine. It can be proved from the second law of thermodynamics that: All reversible engines operating between the same two temperatures have equal efficiency and no engine operating between the same two temperatures can have efficiency greater than this. This theo..

Summary - A sentence is called a statement if it can be adjudged as true or false. Every statement is a sentence, but a sentence may or may not be a statement. A statement involving natural number n is generally denoted by P(n). Principle of mathematical induction states that if P(n) is a statement..

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(..

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..

Probability problems with finite sample spaces Conditional probability Discrete/continuous random variables Mean, variance of discrete random variable Standard distributions Mean, standard deviation of normally distributed random variable Central limit theorem Line..

From the above two theorem, we infer the following (Anti derivative of the function f(x) at b) - (Anti derivative of the function f(x) at a) (ii) The fundamental theorem of integral calculus shows a close relationship between differentiation and integration (iii) These t..

The Normal distribution: Properties of the Normal distribution Using tables of the Normal distribution The Normal distribution as a model for measurements Sampling distributions: Sampling distribution of a sample proportion Sampling distribution of a sample mean Centra..

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..