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| Introduction |
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| Functions are major tools for describing the real world in mathematical terms. For example, the temperature at which water boils depends on the elevation above sea level. The boiling point of water decreases as we ascend, similarly the area of a circle increases as the radius increases. The interest paid on a cash investment depends on the length of time the investment is held. |
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| In each case, the value of one variable y (say) depends on another variable quantity x. y is called dependent variable which depends on the independent variable x. We say y is a function of x. |
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| The concept of limit of a function is one of the basic ideas which distinguishes calculus from algebra and trigonometry. Limits are used to describe how a function f varies. |
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| The concept of limits 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. |
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| 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. |
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Functions Limits and Continuity
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