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Limits, derivatives, infinite series and integrals are a vital part of Mathematics that come under Calculus. Previously called the "Calculus of Infinitesimals", Calculus is the study of change. Calculus today has widespread application in areas like Engineering and Science.
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Calculus is a big step up from Algebra and TutorVista's expert Calculus tutors will guide you in understanding the subject. Precalculus which is the base required to start off with Calculus will be taught to you on a one on one basis with an emphasis on Algebra, Trigonometry and Functions and Geometry. Get a strong foundation and move on to Calculus, starting from defining Limits and L'Hospital's rule to Derivatives which will introduce the student to definition of a derivative to Product and Chain rules and to Integrals and Anti-Derivatives.
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With TutorVista's online tutoring in Calculus, differentiation and integration will not be difficult anymore. Get homework help and unlimited tutoring from TutorVista's online calculus tutoring
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Functions Limits and Continuity |
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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. |
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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. |
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Differentiation |
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The derivative, measures the rate at which the dependent variable changes with respect to the independent variable. It is one of the most important ideas in Calculus. The differentiation of functions are widely used in science, economics, medicine and computer science. |
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Differential Equations |
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Differential Equation: A differential equation is a relation between the independent, dependent variables and their differential coefficients. |
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Indefinite Integrals |
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The expression ∫ f(x) dx |
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is read "the indefinite integral of f(x) with respect to x," and stands for the set of all antiderivatives of f. |
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Thus, ∫ f(x) dx is a collection of functions; it is not a single function, nor a number.
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Definite Integrals |
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Let f (x) be a single valued continuous function defined in the interval [a,b] where b > 0 and let the interval [a,b] be divided into n equal parts each of length h, so that nh = b - a; then we define |
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Application of Derivatives |
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Differential calculus can be considered as mathematics of motion, growth and change where there is a motion, growth, change. Whenever there is variable forces producing acceleration, differential calculus is the right mathematics to apply. Application of derivatives are used to represent and interpret the rate at which quantities change with respect to another variable. |
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Exponential and Logarithmic Series |
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The sum of the infinite series 1 + 1/1! + 1/2! + 1/3! + 1/4! + ...¥ is called the exponential number. |
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If x is any complex number then the series  is called the exponential series. It can be proved mathematically that this exponential series has a sum and we denote it by ex. |
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