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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..
Ordered Pairs and Cartesian Product
In a Rectangular Cartesian System of coordinates the position of a point in a plane is determined by an ordered pair whose elements give the distances from the intersecting straight lines at right angles to each other. These lines are called the axes. The vertical line is called the Y-a..
Co-ordinates
The position of a point with respect to the rectangular axes by means of a pair of numbers is called co-ordinates. The distance OM of point P along x-axis is called x-co-ordinate or abscissa. The distance ON of point P along y-axis is called ordinate or y-co-ordinate. If OM=a an..
Formula
>A number of two digits p and q in that order is 7 greater than the number formed by reversing the digits. The ten's digit is p and the unit's digit is q. Then the number is 10p + q. The number formed by reversing the digits = 10q + p (10p + q) - (10q + p) = 7 A man walks for 'a' hours at x km/hr a..
Linear Equations in One Variable
Let x be the required number. The value of x is determined by solving the equation. Thus \ 2x + x = 36 \ 3x = 36 \ x = 12 \ The number is 12. A man walking at the rate of four kilometres an hour, covers a certain distance in three hours less than another who walks at the rate of three kil..
Worked Examples on Simultaneous Equations
. Find the speed of the boat in still water and the speed of the current. Let the speed of the boat in still water = x km/h, and The speed of the current be = y km/h. Time taken to go down stream = 2 hours Time x Speed = Distance 2(x + y) = 40 x + y = 20 (Divided by 2) (1) Again, the spee..
Calculation of Cell Potential
In an electrochemical cell, electrons flow from negative electrode to the positive electrode. This shows that there is a potential difference between the two electrodes. The minimum potential which causes the flow of the electrons from the negative electrode to the positive electrode is called em..
Dependence of Gravitational Force on Distance
gravitational force between two objects more distant Force of attraction between two bodies of mass m separated by a distance 2d. Let us now calculate the force of attraction when the distance between the bodies is increased three times. Force of attraction between two bodies of mass m separated by a distance 3..
From the top of a spire of height 50 ft, the angles of depression of t..
From the top of a spire of height 50 ft, the angles of depression of two cars on a straight road at the same level as that of the base of the spire and on the same side of it are 25° and 40°. Calculate the the distance between the two cars. => 47 ft or 7.013 ft. or 40.52..
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