Ratio
Ratio is the numerical relationship between two quantities of the same kind. The first quantity is called the antecedent and the second quantity is called the consequent. By performing simple operations on ratios, we get compounded ratio, duplicate ratio, triplicate ratio,..
Ratio and Proportion II
Ratio is the numerical relationship between two quantities of the same kind. The first quantity is called the antecedent and the second quantity is called the consequent. By performing simple operations on ratios, we get compounded ratio, duplicate ratio, triplicate ..
Operations on Sets
The Operations on Sets are: Union of sets, Intersection of sets, Disjoint sets, Difference of two sets (Relative complement), Symmetric Difference of two sets, Complement of a se..
Operations on Matrices
Equality of Matrices - Two matrices are said to be equal if they have the same order and their corresponding elements are equal. e.g., then a = 1, b = 2, c = 3, d = 4, e = 5 and f = ..
Equality of Matrices - Two matrices are said to be equal if they have the same order and their corresponding elements are equal. e.g., then a = 1, b = 2, c = 3, d = 4, e = 5 and f = ..Algebraic Properties of set operations
The Algebraic Properties of set operations are: Idempotent laws, Identity laws, Commutative laws, Associative laws, Distributive laws, De Morgan's Law..
Verification by numerical problems
\ A + B = B + A \ A + B = B ..
\ A + B = B + A \ A + B = B ..To find the sum to infinity of a GP when the common ratio r is numerically less than 1
Consider the GP a, ar, ar 2 ... ..
Consider the GP a, ar, ar 2 ... ..Note 2:
If a and b are positive numbers, then the above method can also be applied to find the numerically greatest term in the expansion of (a - b) n..
Some Applications of Binomial Theorem for Fractional Index
If x be numerically so small that its cube and higher powers may be x 3 , x 4 , x 5 , . are all approximately zero. If x be numerically so small that its square and higher powers may be neglected, then (1+x) n = 1+nx (approximately), because x 2 , x 3 , x 4 ,. are all appr..
If x be numerically so small that its cube and higher powers may be x 3 , x 4 , x 5 , . are all approximately zero. If x be numerically so small that its square and higher powers may be neglected, then (1+x) n = 1+nx (approximately), because x 2 , x 3 , x 4 ,. are all appr..Example:
If x be numerically so small that its cube and higher powers may be neglected, then find the binomial expansions for: i) (1 + 2x) - 4 ..
If x be numerically so small that its cube and higher powers may be neglected, then find the binomial expansions for: i) (1 + 2x) - 4 ..See what our Users say :
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