# Limits and Derivatives

## The expected value of the function as dictated by the points to the left of a point defines the left hand limit of the function at that point. Similarly the right hand limit. Limit of a function at a point is the common value of the left and right hand limits, if they coincide. Calculus is that branch of mathematics which mainly deals with the study of change in the value of a function as the points in the domain change. An exponential function is a function of the form y = abx , where both ‘a’ and ‘b’ are greater than ‘zero’, ‘b’ is not equal to one and x is any real number. Limit: Let f be a real valued function. The limit of f(x) at some point ‘a’ is the number L which this function attains when x gets closer and closer to ‘a’. Limit of the sum or difference of two functions is the sum of the respective limits of both the functions. Limit of the product of two functions is the product of the respective limits of both the functions. Limit of the division of two functions is the quotient of the respective limits of both the functions. There are some of the standard limits which are algebraic functions and trigonometric functions. There are some of the standard derivatives given below: d/dx (xn) = nxn-1 d/dx (sinx) = cosx d/dx (cosx) = –sinx

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