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Exponential and Logarithm Equations : In this section we'll learn solving equations along with exponential functions or logarithms in them. We'll begin with equations which invol
Two tangents PA and PB are drawn to the circle with center O, such that ∠APB=120 o . Prove that OP=2AP. Ans: Given : - ∠APB = 120o Construction : -Join OP To prove : -
There may be more than one independent variable which determines the value of y. The dimension of a function is determined by the number of independent variables in the
a couple q''s
particular solution of equation y''''-3y''-4y=2sinx
The 3-D Coordinate System We will start the chapter off with a quite brief discussion introducing the 3-D coordinate system and the conventions that we will be utilizing. We
The Cartesian product (also called as the cross product) of two sets A and B, shown by AΧB (in the similar order) is the set of all ordered pairs (x, y) such that x€A and y€B. What
HE IGHTS AND DISTANCES If the angle of elevation of cloud from a point 'h' meters above a lake is α and the angle of depression of its reflection in the lake is β , prove
a) Let n = (abc) 7 . Prove that n ≡ a + b + c (mod 6). b) Use congruences to show that 4|3 2n - 1 for all integers n ≥ 0.
Properties of Logarithms 1. log a xy = log a x + log a y 2. = log a x - log a y 3. log a x n = n log
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