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A statement of a limit is "the limit as x approaches (some x value) of the function f(x) is exactly equal to (some y value), which we write as limx?(some x value)f(x)=(some y value). For example, limx?5(x2?2)=23. This is the most important idea in all of calculus.

The limit value typically has two types of values, namely, the Left-hand Limit and the Right-Hand Limit. Thus, Left-Hand Limit: limx?a?f(x)=limh?0f(a?h) Right-Hand Limit: limx?a+f(x)=limh?0f(a+h)

Derivatives Formula. f?(x) = limx?a f(x + h) ? f(x) / h is referred to as the f at x if derivative limx?a f(x + h) - f(x) / h exists on a finite scale. For function f, its derivative is defined as f?(x), assuming the existence of the aforementioned equation.

The limit formula is the representation of the behavior of the function at a specific point and the formula analyzes that function. Limit describes the behavior of some quantity that depends on an independent variable, as that independent variable approaches or comes close to a particular value.

Limits formula:- Let y = f(x) as a function of x. If at a point x = a, f(x) takes indeterminate form, then we can consider the values of the function which is very near to a. If these values tend to some definite unique number as x tends to a, then that obtained unique number is called the limit of f(x) at x = a.

The two definitions of a derivative are as follows: By the geometrical approach: The slope of the curve for the given function is called the derivative of a function. By physical approach: The instantaneous rate of change of a function concerning the variable at a point is called the derivative of a function.

The list of basic integral formulas is given below: ? 1 dx = x + C. ? a dx = ax+ C. ? xn dx = ((xn+1)/(n+1))+C ; n?1. ? sin x dx = ? cos x + C. ? cos x dx = sin x + C. ? sec2x dx = tan x + C. ? csc2x dx = -cot x + C. ? sec x (tan x) dx = sec x + C.

Definition: limit of a function of two variables if for each ?>0 there exists a small enough ?>0 such that for all points (x,y) in a ? disk around (a,b), except possibly for (a,b) itself, the value of f(x,y) is no more than ? away from L (Figure 14.2.