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Calculus is the study of change. Calculus has widespread application in areas like Engineering and Science. Since the study of Calculus is pivotal in branching out to other fields, it is important to get the best Calculus help right from the formative years itself.
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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.
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.
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.
Differential Equation: A differential equation is a relation between the independent, dependent variables and their differential coefficients.
The expression ∫ f(x) dx is read "the indefinite integral of f(x) with respect to x," and stands for the set of all antiderivatives of f.
Thus, ∫ f(x) dx is a collection of functions; it is not a single function, nor a number.
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
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.
The sum of the infinite series 1 + 1/1! + 1/2! + 1/3! + 1/4! + ...¥ is called the exponential number.
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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