Binomial Theorem

Basic Mathematical ConceptsBinomial TheoremIf x lies between -1 and +1 then, WhereIf n is a positive integer then the expression has (n+1) terms.If n is a negative integer then the expression has infinite terms.Now if x<<<1, i.e. if x is much smaller than 1, then the terms containing higher powers of x can be neglected and thus only the first two terms are important. Thus, Expand the following using Binomial theorem.Now try solving the following problems using Binomial theorem. (up to two decimal places)If the acceleration due to gravity at a height h above the surface of the earth (radius R) is given by If h <<< R, then prove that DifferentiationDifferentiation of y with respect to x is defined as the ratio of the change in y to the change in x, when the change in x, when the change in x is extremely small (∆x → o).Rules of differentiationIf y = C where c is a constant, then, If y = then, If y = C, then, If y = u ± v ± w ± --------- where u, v, w,------- are the the functions of x, then, If y = uv where u and v are the functions of x, then, If y = , where u and v are functions of x, then,