*Parabola
Parabola is an open figure & can be defined as the locus of a point P which moves in a plane so that its distance from a fixed point (called Focus, F) bears a constant ratio (called eccentricity, e = 1) to its distance from a fixed straight line (called directrix).
*Mean of n terms
If x1, x2, _ _ _ _ _ _ _ _ _ , xn be n quantities then their
If A, G and H be A.M., G.M. and H.M. between two numbers, then
(a) A ³ G ³ H,(b) G2 = A .H
Series
*Logarithms
Let a is an arbitrary positive real number except 0. If ax = y, then logay = x
Conversely, the antilogarithm of x is the number y i.e. y = antilogax.
Here ax = y is called arbitrary exponential function and loga y = x is read is log of y to the base a is equal to x. If a = 10, log is called common & if it is e, then called natural.
*Periodic functions
A function is said to be periodic if it repeats itself after a fixed period. For a periodic function f (x) there exists a positive number ‘p’ such that
f (x + p) = f (x) for all x.
The smallest such value of ‘p’ is called period.
Periodicity of tan θ & cot θ is π & that of sinθ, cosθ, cscθ and secθ is 2π.
*Semi angle formulae
<Angle measurement
^A long horizontal fixed wire carries a current of 100 A. Directly above and parallel to it is another wire carrying a current of 20 A and weighing 0.04 N/m. The separation between the two wires so that the upper wire is just supported by the magnetic repulsion is
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