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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..
Problems on Simultaneous Equations
Solve the following Systems of linear equations : 1. If one number is thrice the other and their sum is 60, find the numbers. 2. Find the fraction which becomes 1/2 when the denominator is increased by 5 and is equal to 1/3 when the numerator is diminished by 4..
Indices and laws of indices
Indices - If m is a positive integer, a x a x a .. m times is written as am. a is called the base and m is the power. We read it as "a raised to the power m". The power is also called "the index" or "the exponent". When the power or index is a fraction say then and it is a surd of order n..
Indices - If m is a positive integer, a x a x a .. m times is written as am. a is called the base and m is the power. We read it as "a raised to the power m". The power is also called "the index" or "the exponent". When the power or index is a fraction say then and it is a surd of order n..Worked Examples on Simultaneous Equations
Find the fraction which becomes when the denominator is increased by 5 and is equal to when the numerator is diminished by 4. Let the fraction by When y is increased by 5, fraction becomes or 2x = y +..
Find the fraction which becomes when the denominator is increased by 5 and is equal to when the numerator is diminished by 4. Let the fraction by When y is increased by 5, fraction becomes or 2x = y +..Algebraic identity
An algebraic identity is a statement of equality between two algebraic expressions, but it is satisfied for all values of the variabl..
Linear inequations
An inequation is said to be linear if each term of the algebraic expression (or expressions) of the inequation contains first degree variables (not the product of variables..
Linear equations in two variables
A Linear equation is a first degree algebraic expression with one,two or more variables equated to a constant. Graphically a linear equation with one or two variables is a straight line whereas one with three variable represents a plane. A simple linear equation is a statement of equ..
Simultaneous Equations
Simultaneous Equations - A linear equations in two variables x and y is of the form ax + by + c = 0 ( ) where a, b, c are real numbers. To find a solution for this equation, we can assign any value for one of the variables and find the value of the other variable such that the two sides of the equa..
Simultaneous Equations - A linear equations in two variables x and y is of the form ax + by + c = 0 ( ) where a, b, c are real numbers. To find a solution for this equation, we can assign any value for one of the variables and find the value of the other variable such that the two sides of the equa..Linear Equations in One Variable
An equation is an equality connecting some unknowns. The unknowns are represented by "letters" and are called "the variables". If the equation has only one unknown, it is called "an equal in one variable". The word "Linear" means "of degree one". Hence if only a single variable with degree one oc..
Result
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