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Integration
We have, so far, seen that differential calculus measures the rate of change of functions. Differentiation is the process of finding the derivative (rate of change) of a function F(x) and is denoted by F'(x) Often, we may know the rate of change, F'(x) of a function F(x) which is unknown to us. In such situations we would like to find out the original function F(x) from the derivative, F'(x). Reversing the process of differentiation and finding out the original function from the derivative is called integration. The original function, F(x) is called the integral.
The left hand side of the equation is read as "the indefinite integral of f(x) with respect to x. The symbol is the integral sign, f(x) is the integrand and 'c' is an arbitrary constant. The arbitrary constant 'c' is added because of the following reason:
If d/dx {F(x)} = f(x) then we can also write that d/dx {F(x) + c} = f(x) where 'c' is an arbitrary constant, because the derivative of any constant is zero.
1. a) Given a digraph G = (V,E), prove that if we add a constant k to the length of every arc coming out from the root node r, the shortest path tree remains the same. Do this by
$36.00*6/36+(-$3.60)x30/36
Suppose research on three major cell phones companies revealed the following transition matrix for the probability that a person with one cell phone carrier switches to another.
Find the 35th term of the sequence in which a1 = -10 and the common difference is 4.
tan 2x = 1
Business Applications In this section let's take a look at some applications of derivatives in the business world. For the most of the part these are actually applications wh
Given the hypotenuse of a right triangle: Given that the hypotenuse of a right triangle is 18" and the length of one side is 11", what is the length of another side? a 2 +
Suppose S = {vi} and T = {ti} are "easy" sets of knapsak weight. Also, P and q are primes p > ?Si and q > ?ti. We can combine S and T into a signle set of knapsack weight as follow
Solve the following Linear Programming Problem using Simple method. Maximize Z= 3x1 + 2X2, Subject to the constraints: X1+ X2 = 4 X1+ X2 = 2 X1, X2 = 0
FIRST OF ALL I WANNA KNOW THECHNIQUES, I CAT DIVIDE BIG BIG NUMBERS , EVERYTHING IN MATH IIS VERY HARD FOR ME I HOPE YOU CAN HELP ME
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