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Calculus consists of four basic topics limits derivatives indefinite integrals and definite integrals These topics build upon one another with out adequate knowledge of one it is difficult to master the others The concepts we grasp in this course are useful for many professions and can be used to interpret many types of problems that may at first seem intimidating but soon become second nature With the aid of a graphing calculator we can now solve more complex problems than in the past Calculus students today are capable of accomplishing much more within the field than ever thought possible The topic that forms the basis for calculus is that of limits Hence a background in analysis the study of limits is crucial to any individual wishing to explore the world of calculus Basically the limit of a function f as x approaches a value c is the y-value fx stays close to when x is kept close enough but not equal to c Since limits of functions can be used to define each of the other three concepts involved in calculus one should become confident in their knowledge of limits before learning about integrals and derivatives In taking a calculus course the student studies the concept of limit in four different ways graphically numerically algebraically and verbally Throughout the study of limits one learns about many related topics including limit theorems continuity limits involving infinity and the intermediate value theorem among others These act in unison to form the foundation required for the study of the other topics in calculus In addition to limits derivatives are vital to calculus as they serve many purposes within the field Physically a derivative is the slope or instantaneous rate of change of a function An important real-would application for derivatives is to easily find the displacement velocity and acceleration of a given object Derivatives can also be used to find the maximum and minimum values of a function
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