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Extrema : Note as well that while we say an "open interval around x = c " we mean that we can discover some interval ( a, b ) , not involving the endpoints, such that a < c < b . Or, in other terms, c will be contained somewhere within the interval and will not be either of the endpoints.
Also, we will collectively call the minimum and maximum points of a function the extrema of the function. Thus, relative extrema will refer to the relative minimums & maximums whereas absolute extrema refer to the absolute minimums & maximums.
1. Suppose n ≡ 7 (mod 8). Show that n ≠ x 2 + y 2 + z 2 for any x, y, z ε Z. 2. Prove ∀n ε Z, that n is divisible by 9 if and only if the sum of its digits is divisible by 9.
prove that s is bounded?
DEVELOPING ESTIMATION SKILLS : A study was done with some Class 3 and Class 4 children of five village schools to gauge how well they had understood the standard algorithms. The
Find out the volume of the solid obtained by rotating the region bounded by y = (x -1) ( x - 3) 2 and the x-axis about the y-axis. Solution Let's first graph the bounded r
A painting was purchased 11 years ago for $26900. It has just been sold for $78000. Calculate the flat rate of appreciation p.a.
Derivatives The rate of change in the value of a function is useful to study the behavior of a function. This change in y for a unit change in x is
What is Plotting Points? To "plot" or "graph" values means to find points on a number line. The numbers four, negative two, negative three, zero, two, and negative four are bei
add 1 and 20 over 40 with 2 and 30 over 50
Bayes’ Theorem In its general form, Bayes' theorem deals with specific events, such as A 1 , A 2 ,...., A k , that have prior probabilities. These events are mutually exclusive
INTRODUCTION : Do you remember your school-going days, particularly your mathematics classes? What was it about those classes that made you like, or dislike, mathematics? In this
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