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Why is it important that you be able to use series like the Maclaurin to approximate the behavior of various functions?
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Are graphs useful for describing functions?
YES! Simply by taking a quick glance at a graph, you can see several characteristics of the function: local minimums/maximums, points of inflection, end behavior, asymptotes, etc etc... If you wanted to find these without the graph, you would have to do some math which might end up being very time consuming for very complicated functions. Even worse: what if the function is not elementary, and you can't express it in terms of finite arithmetic operations?
What is difference between OOA and OOD?
ooa -identify the object ood -implement the identified object. ooa -analysis phase ood -design phase ooa -expose the behavior of the object ood -hide the behavior of the object ooa -what to develop ood -how to develop
Why was the calculus student confused about y equals ex and the derivative of y equals ex?
Because the derivative of e^x is e^x (the original function back again). This is the only function that has this behavior.
What is the concept of a limit in calculus?
In calculus, limits are extremely important because calculus itself is based upon limits. Basically, a limit describes the behavior of a dependant variable when its independent variable takes extreme values.For example, lets consider this function : y =1/x. As you know, this typical function is not defined at x = 0 because the division by zero is not admitted in real numbers. Therefore we cannot compute the value of y when x = 0. However, we can observe how the function behaves near x = 0 : this is the concept of limit. Lets see how this function behaves when x approaches zero from the right:limx->0+ 1/x = infinityYou can verify this limit by substituting x with values that approach zero: 1/0.1 = 10; 1/0.000009 = 11,111.11; ... When x takes extremely small values, y takes extremely large values. If we repeat this process forever, we will say that, at the limit, y will have an infinite value. That's what the limit is.Two of the most important uses of limits in calculus are derivatives/differentials and integrals. For example, the derivative of a function is the limit of the function's ratio of variation of dependant and independent variables as the variation of the independent variable approaches zero:derivative of f(x) with respect to x = f'(x) = d[f(x)]/dx ...Also, a definite integral is defined as the limit of the sum of infinitely small elements as the number of elements approaches infinity.To calculate limits, you must have a good knowledge of the "algebra of infinity" (infinity + infinity = infinity, sqrt(infinity) = infinity, ...).Of course, this is a very basic description of the limit concept; there are many, many cases where the limit is tricky to calculate.The concept of Functions limits and Continuity leads to define and describe continuity and derivative of the function.The continuity of a function has practical as well as theoretical importance. We plot graphs by taking the values generated in the laboratory or collected in the field. We connect the plotted points with a smooth and unbroken curve (continuous curve). This continuous curve helps as to estimate the values at the places where we haven't measured. It was developed by Isaac Newton and Leibnitz.Here in this chapter, we will study some standard functions, their graphs, concept of limits and discuss about the continuity of the functions. Throughout this chapter, we denote R as the set of real numbers.Types of Limit:Left Hand Limit: Let f(x) tend to a limit l1 as x tends to a through values less than 'a', then l1 is called the left hand limit.Right Hand Limit: Let f(x) tend to a limit l2 as x tends to 'a' through values greater than 'a', then l2 is called the right hand limit.We say that limit of f(x) exists at x = a, if l1 and l2 are both finite and equal.
Should you check the value of a function on its asymptote to get a good idea of how its graph should look?
The asymptote is a line where the function is not valid - i.e the function does not cross this line, in fact it does not even reach this line, so you cannot check the value of the function on it's asymptote.However, to get an idea of the function you should look at it's behavior as it approaches each side of the asymptote.
What are functions of behavior?
what are the functions of behavior
What are the macro functions of communication?
Macro functions of communication means the basic and the important functions of communication. These functions are much more significant than the micro functions of communication. These functions include: 1.The emotive functions which deal with communicating inner states and emotions. 2.The Directive functions to affect the behavior of others etc.
Why are asymptotes important characteristics of rational functions?
Asymptotes are one way - not the only way, but one of several - to analyze the general behavior of a function.
psychology?
the scientific study of human behavior and mind functions
Why is it important to understand a child's behavior?
it is important to understand a child's behavior so you know how to deal with it.
What can be summarized as the ability to plan and carry out behavior and to solve problems?
Executive functions
What are the essential components of an effective MIS and why in Management Functions and Behavior?
Calibri (Body)
How are hormones important in cellular communication?
By bind with specific receptors, the hormones are able to regulate reproduction, development, energy metabolism, growth, and behavior. The reason why it is important that these functions be activated through hormones (a signaling molecule) is because there is an exact time that these functions need to happen. A caterpillar can't start changing into a butterfly if it hasn't finished its cacoon yet.
How do you do linear functions?
By finding something who's behavior is represented by a linear function and graphing it.
Why human behavior in an organization important as a teacher?
Human behavior is very important in an organisation. It is because like a teacher, the human behavior also teaches us variety of things.
Is it important to make generalisation of behavior?
no
Which of Cato's objections to women's behavior do you think was the most important?
which of catos objections to womens behavior do you think was most important
