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Logarithmic functions have the following general properties
If y = loga x, a > 0 and a ≠1, then
The domain of the function is the set of all positive real numbers and the range is the set of all real numbers.
For base a > 1, the function is increasing and concave and for 0 < a < 1, the function is decreasing and convex.
For all bases, y = 0, if x = 1
Telescoping Series It's now time to look at the telescoping series. In this section we are going to look at a series that is termed a telescoping series. The name in this c
Find the value of p and q for which the system of equations represent coincident lines 2x +3y = 7, (p+q+1)x +(p+2q+2)y = 4(p+q)+1 Ans: a 1 = 2, b 1 = 3, c 1 = 7 a 2 =
In the introduction of this section we briefly talked how a system of differential equations can occur from a population problem wherein we remain track of the population of both t
Expected opportunity loss or EOL method EOL method is aimed at minimizing the expected opportunity loss or OEL. The decision maker chooses the strategy along with the minimum e
if the sum of lengths of hypotenuse and a side of right triangle are given, prove the area of the triangle is maximum when angle between them is pi/3
info about right triangles
Decision Trees And Bayes Theory This makes an application of Bayes' Theorem to resolve typical decision problems. It is examined a lot so it is significant to clearly understan
in triangle abc ab=ac and d is a point on side ac such that bc*bc=ac*cd. prove that bc=bd
Find the sum of a+b, a-b, a-3b, ...... to 22 terms. Ans: a + b, a - b, a - 3b, up to 22 terms d= a - b - a - b = 2b S22 =22/2 [2(a+b)+21(-2b)] 11[2a + 2b - 42b] =
Solving an equation using Multiplication and Division A variable is a symbol that represents a number. Usually we use the letters like n , t , or x for variables. For
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