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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.
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A painter leans a 10-foot ladder against the house she is to paint. The foot of the ladder is 3 feet from the house. How far above the ground does the ladder touch the house? Appro
Write a program to find the area under the curve y = f(x) between x = a and x = b, integrate y = f(x) between the limits of a and b. The area under a curve between two points can b
OTHER WAYS TO AID LEARNING : Here we shall pay particular attention to the need for repetition, learning from other children, and utilising errors for learning.
Vectors This is a quite short section. We will be taking a concise look at vectors and a few of their properties. We will require some of this material in the other section a
Find the generating function for the number of r-combinations of {3.a, 5.b, 2.c} Ans: Terms sequence is given as r-combinations of {3.a, 5.b, 2.c}. This can be writte
show that all primes except 2, are of the form 4n-1 or 4n+1
Example Find the Highest Common Factor of 54, 72 and 150. First we consider 54 and 72. The HCF for these two quantities is calculated as follows:
Horizontal tangents for Parametric Equations Horizontal tangents will take place where the derivative is zero and meaning of this is that we'll get horizontal tangent at value
A lobster catcher spends $12 500 per month to maintain a lobster boat. He plans to catch an average of 20 days per month during lobster season. For each day, he must allow approx
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